A Text-Book of Mechanical Drawing, And Elementary Machine Design

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WORKS OF JOHN S. RED)

PUBLISKBD BY

JOHN WILEY & SONS.

A CourM In Mechanical Drawing. Third Edition. Revised and Enlarged. 8vo. viii -f- 186 paces. 233 figures. Cloth. $2.00. Mechanical Drawing and Elementary Machine

Design. By John 8. Reid, Professor of Mechanical Drawing, Armour Institute of Technology, and David Reid, formerly Instructor in Mechanical Drawing, Sibley College, Cornell University. Second Edition Revised and Enlarged. 8vo. xii-f-439 pages. 329 figures. Cloth, $3.00.

?^

A TEXT-BOOK

OP

MECHANICAL DRAWING

AND

ELEMENTARY

MACHINE DESIGN

BY JOHN S. REID, Jtfiructor in MeeKantcal Drawing and Machine De»iffn, -*Armour JnatituU of Technology; Member of the American Society of Mechanical Bngineert; AND

DAVID REID,

Formerly Inttructor in Meehanieal Drawing and Designing, Sibley College, Cornell University, Ithaca, N. Y.

SECOND EDITION, REVISED AND ENLARGED. TOTAL ISSUE, EIGHT THOUSAND.

NEW YORK: JOHN WILEY & SONS. London : CHAPMAN & HALL. J^imited.

1909. -' V' • • '

THE NEW YORK PUBLIC LIBRARY 388629 A A8TOR. LENOX AND TILDEN FOUNDATIONS H 1928 L

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PREFACE TO THE SECOND EDITION.

The increasing use of this book for students of all kinds of engineering, in teaching machine drawing and elementary machine design, and the changes which have naturally occiured since the first edition was published, have made a revision and the following additions both necessary and desirable. Course II has been prepared for students in machine drawing and elementary machine design who have completed the full course given in "A Course in Mechanical Drawing/^ by John S. Reid, published by John Wiley & Sons, New York, or its equivalent.

The number of problems, their scale and size, have been selected to properly fill a certain size of sheet, together with notes, bill of material, and title. New cuts have been introduced illustrating bills of material and titles, with dimensions for construction. A decidedly new feature has been introduced here in giving the minimum time allowed for finishing each plate according to directions in the text, and should be much appreciated by Instructors when determining the amount of work to require from their students in any given term. The time allowed to finish the different plates has been carefully determined, and any 111

IV PREFACE. Student of fair intelligence who will honestly try can finish any of the plates in the time given. The Course in Lettering has been added for the benefit of students who have not had its equivalent in their preparatory course in mechanical drawing. Course III is a short course which has been added here as a supplement to Course II, and consists of practical machine sketching, the making of working drawings from sketches, isometrical drawing of a lay-out of piping, and machine design. The report on the " Present Practice in Drafting Room Methods," which will be found at the end cf the book, is also new, and will interest Instructors and enable them to adopt a system in their drawingj courses that may closely approximate the best practice in the leading and most progressive drafting rooms in the United States, , The thanks of the authors are due and are most cordially extended to those who have used this book in the past and have encouraged and assisted them by gracious words and timely suggestions.

John S. Reid. D. Reid. AKMOUR iNStlTUTE or TrXHNOLOGY, Chicagt), III., September, 1908.

PREFACE.

To properly prepare students for advanced machine design it has been found necessary to introduce a course designed to apply the principles of mechanical drawing to the solution of practical problems in machine construction and to familiarize the student with the arrangement and proportions of the most important machines and their details recognized by competent engineers to be the best practice of the present time. It is essential to intelligent study and an economical expenditure of time and labor that^ before attempting to design a new machine or improve an old one, the student should post himself with all possible information concerning what has already been done in the same direction. To. this end the present work has been prepared. In it we have attempted to show what is the best United States practice in the design and construction of various machines and details of machines, using rules and formulae whenever feasible in working out practical problems. In addition to this will be found the latest and most approved drafting-room methods in use in this country, without which most drawings would be practically useless. Up ^TO the present time no text-book that we know of has been CO X oo C9

VI PREFACE. published in the United States that could in the best way fill the need as explained above.

Books of a somewhat similar nature have been published in Great Britain, showing that the same need has been felt there as here. These books; modified to suit American practice, have been used to some extent in this country because they were the best to be had, but are not by any means all that can be desired for our purpose in their present form. While preparing this course for the sophomore students in Sibley College the authors endeavored to secure samples of the actual machines ox parts of machines as collateral in illustrating the exercises given in the book, with a result that in our drafting-rooms we have many examples of modern machine construction placed convenient to the students' hands, so that they may examine and handle the actual thing itself while solving the problems in drawing and designing. This we believe of great importance in the study of machine design and construction, because few are able to describe a machine even with the assistance of a drawing so well as to enable the student to conceive it in his mind as it actually is. The preparation necessary for the proper understanding and execution of the problems contained in this book is as follows: use of instruments, instrumental drawings applied to drawing geometrical problems in pencil and ink, thorough knowledge of the conventional lines, hatch-lining and colors for sections, mechanical and free-hand lettering, orthographic projection in the third angle, isometrical drawing — in brief all that is contained in ** A Course in Mechanical Drawing,** by John S. Reid, published by John Wiley & Sons, New York. In the preparation of the drawings for this work we are

PREFA C£. vii indebted to many of the leading engineering firms of this and other States, who have kindly supplied us with drawings and samples of the latest and best practice of the day. Our thanks are especially due to the Dodge Manufacturing Com* pany, the Detroit Screw Works, the Buckeye Engine Co., the United States Metallic Packing Co., the National Tube Works, the Ridgeway Dynamo & Engine Co., the Murray Gun Works, Henry R. Worthington, Robt. Pool & Sons, the Baldwin Locomotive Works, the Schenectady Locomotive Works, the American Pulley Co., the Hyatt Roller BearingCo., the Macintosh and Seymour Engine Co., and many others. Our acknowledgments are also due to many of the best authorities on the different subjects treated, among which may be mentioned Thurston's " Materials of Construction,"

A. W. Smith's ** Machine Design," Klein's " Machine Design," Unwin's '* Machine Design," Barr's " Boilers and Furnaces," Peabody and Miller's "Steam Boilers," Low and Bevis's ** Drawing and Designing," John H. Barr's Kinematics," Thurston's "Steam Boilers," Reuleaux's Constructor," the '* Proceedings of the American Railwa}^ Master Mechanics' Association," etc., etc. J. S. R. D. R.

CONTENTS.

INTRODUCTORY INSTRUCTIONS. J. S. R. PAGE Mechanical Drawing i Complete Outfit 2 Use of Instruments 7 Shade-lines and Shading 15 Working Drawings 17 Lettering iq Figuring 19 Standard Conventions 20 Cross-sections 26 Constructions 26 Elementary Machine Design 29 Materials op Construction 30 Strength op Materials 36

Useful Tables, etc 41 CHAPTER I. D. R. Screws, Nuts, and Bolts 48 CHAPTER II. D. R. Keys, Cotters, and Gibs 109 CHAPTER III. J. s. R. Rivets and Riveted Joints 125 CHAPTER IV. J. S. R. Shafting and Shaft-couplings 157 iz

X CONTENTS. CHAPTER V. J. S. R. Pipes and Pipe-coupungs i8^ CHAPTER VI. D. R. Bearings, Sole-plates, and Wall Box-frames 206 CHAPTER VII. J. s. r. Belt Gearing 238. CHAPTER VIII. J. s. r. Toothed Gearing 262 CHAPTER IX.

J. S. R. Valves, Cocks, and Oil-cups 278CHAPTER X. J. S. R. & D. R. Engine Details 305:

Elementary Machine Drawing (Course II) 38J (Course III) 39) Present Practice in Drafting Room Conventions and Methods in Making Practical Working Drawings 419.

SUGGESTED COURSES. FALL TERM. X. Ex. I, 3, 4. 5.6, 7, lo. la. 13. 15. 19. 22. 24, 26, 29. 30. 3a. 34, 38, 40, 46. 51. a. Ex. 2. 3. 4, 5, 6. 8, 10. II. 14. 16, 18, 20. 24. 27» 29. 31, 33. 35. 39, 41, 47. 51. 3. Ex. I, 3. 4. 5. 6. 8, 9, 12. 13. 17. 19. 22. 23. 25. 29. 30. 32, 34, 38, 42, 48. 5>. 4. Ex. 2. 3. 4. 5. 6, 7. 9. II. 14, 15, 18. 21, 24. 28, 29. 31, 33. 36, 38, 43, 49. 51. 5. Ex. I. 3. 4. 5. 6. 8, 10. 12. 13. 16. 19, 22, 23, 26, 29. 30. 32. 34. 38, 44« 50. 52. 6. Ex. 2. 3. 4. 5. 6, 7. 9. ". M. 17. 18. 21. 24. 27. 29. 31. 33, 37. 39, 45, •50. 52. Fall Term Continued. 1. Ex. 52, 54. 59. 64. 68, 73. 77. 86. 89. 90, 93. a. Ex. 52, 55. 60. 65, 70, 74. 84. 87. 90. 92. 94.

3. Ex. 52. 54, 61. 66, 71, 75. 85. 88, 90, 91. 93. 4. Ex. 52, 56, 62. 67. 70. 76, 84, 86. 90, 92, 94. 5. Ex. 53. 57. 63. 68. 71, 77. 85. 87, 90. 91. 93. 6. Ex. 53. 58. 64. 69 72, 76, 84. 88, 90, 92, 94. WINTER TERM. X. Ex. 95. 97. 99. io». 103, 106, 108, III, 113. 117. 119. 121. 124, 130, 136. 139. 142. 145. 147. 149a. Ex. 96, 98, 100, 102. 104, 105, 107. 112. 114, 118, 120, 122, 125, 131, 137. 140. 143. 146, 148. 1493. Ex. 95. 97. 99. loi. 104. 107. no, 112. 115, 117. 121, 123. 126. 132, 138. 139. M2. 145. 147. 140. 4. Ex. 96, 98, 100. 102. 103. 106, 108. Ill, 113, 116. 119. 122, 127, 133, 136, 138. 144. 146. 148. 1495. Ex. 95. 97. 99, loi. 104, 105, 108. Ill, 113. 116. 120. 121, 128. 134, 137. MO, 142. 145. 147. 1496. Ex. 96. 98, 100. 102. 106, 107. no. 112. 115. 117. 119, 122. 129, 135, 136. 138. 143. X46, 148. 149.

3 DSAWING AND DESiGNtNG. from rules and formulae, will induce the student to think, and tend to develop any natural ability he may have in this direc* tion. It has been the aim of the authors in the arrangement of problems to accomplish this purpose in the highest degree possible. The following notes on the complete outfit of instruments -and materials should be consulted before buying, because it is very essential to the best results that a good outfit be secured. . The outfit for students in mechanical and machine drawing is as follows:

(i) The Dkawing-board for academy and freshman work is i6"X2i"Xj'% the same as that used for free-hand drawing. The material should be soft pine and constructed as shown by

(z) I Scribbling Pencil with rubber tip. (3) Pencils, one 6H and one 4H Koh-i-noor or Faber. (4} The T-Square; a plain pcarwood T-square with a fixed hra;l is all that is necessary. ~ Length 21". (5) iNSTBaMENTS. "Pocket Book" Set, shown by Fig. 2, recommended as a iirst-class medium-priced set of instruments. Il contains A CoupASS, si" long, with fixed needle-point, pencil, pen

tSTRODVCTORY INSTRUCTIONS. 3 and lengthening bar; a Spring Bow Pencil, 3" long; a SpsniG Bow Pen. 3" long; a Spring Bow Spacer, 3" long;

\ Drawing-pens, merfium and small, i Hair-spring Divider. 5^ iong; a nickcl-plaled box widi leads.

B^5

.'\»^y

Fig, 3. (6) A Triangular Boxwood Scale graduated as follows: ' and 2", 3" and i}", 1" and V', \" and |", I'n" and r"/', (7) I Triangle 30°X6o*', ceiluUid, ro" long. Fig. 4. I '■^go, " 7" " (8) 1 iBRF.firi-AR Curve. No. 13. Fig. 5,

(9) Emerv Pencil Pointer. (to) Ink, black walcrproof. Fig, 7(11) Ink Eraser, Faber's Typewriter. No. 104.

DRAWING AND DESIGNING.

(12) Pencil Esases, "Emerald" No. 211. Fig. 9. (13) Sponge Rubber or Cdbe of "Abtgum." Figs. lo, it.

(14) Tacks, a small carton of i oz. copper tacks, and i doz. small thumb larks. (15) Arkansas Oil Stone. 2"X1"XiV". {16} Protractor, German silver, about 5"diam. Fig. 12. (17) Scale Goahd, " " Fig. 13.

DRAWING AND DESIGNING.

(i8) 2 sheets ot *' Cream*' Drawing Paper. (19) 2 '' '* Imperial Tracing Cloth. (20) I Cross-section Pad. 8"Xio". (21) I Scribbling Pad.

.//

IS''X20

//

.//

//

I5''X20''.

Fio. la. Fto. 13. (22) i> Erasing Shield, nickel plated. (23) 2 Lettering Pens, "Gillott" No. 303. (24) 2 '' ' * " Ball Point," No. 506. (25) 2 '' '' ** '* No. 516. (26) I Two-foot Rule

INTRODUCTORY INSTRUCTIONS.

INSTRUMENTS. It is a common belief among students that any kind of cheap instrument will do with which to learn mechanical drawing, and not until they have acquired the proper use of the instrunients should they spend money in buying a firstclass set. This is one of the greatest mistakes that can be made. Many a student has been discouraged and disgusted because, try as he would, he could not make a good drawing, using a set of instruments with which it would be difficult for even an experienced draftsman to make a creditable showing. If it is necessary to economize in this direction it is better and easier to get along with a fewer number, and have them of the best, than it is to have an elaborate outfit of questionable quality. The instruments shown in Fig. 2 are well made of a moderate price, and with care and attention will give good satisfaction for a long time.

USE OF INSTRUMENTS. The Pencil. — Designs of all kinds are usually worked out in pencil first, and if to be finished and kept they are inked in and sometimes colored and shaded ; but if the drawing is only to be finished in pencil, then all the lines except construction^ center, and dimension lines should be made broad and dark.

8

VKA WING AND DESIGNING.

SO that the drawing will stand out clear and distinct. It will be noticed that this calls for two kinds of pencil-lines, the first a thin, even line made with a hard, fine-grained leadpencil, not less than 6H (either Koh-i-noor or Faber's), and sharpened to a knife-edge in the following manner: The lead should be carefully bared of the wood with a knife for about \'\ and the wood neatly tapered back from that point; then lay the lead upon the emery-paper sharpener illustrated in the outfit, and carefully rub to and fro until the pencil assumes a long taper from the wood to the point ; now turn it over and do the same with the other side, using toward the last a slightly oscillating motion on both sides until the point has assumed a sharp, thin, knife-edge endwise and an ell^tical contour the other way. This point should then be polished on a piece of scrap drawing-paper until the rough burr left by the emery-paper is removed, leaving a smooth, keen, ideal pencil-point for drawing straight lines. With such a point but little pressure is required in the hands of the draftsman to draw the most desirable line, one that can be easily erased when necessary and inked in to much better advantage than if the line had been made with a blunt point, because, when the pencil-point is blunt the inclination is to press hard upon it when drawing a line. This forms a groove in the paper which makes it very difficult to draw an even inked line. The second kind of a pencil-line is the broad line, as explained above; it should be drawn with a somewhat softer pencil, say 4H, and a thicker point. All lines not necessary to explain the drawing should be.

/XTKODlCrOFV IXSTKUCTIOl^S. 9 erased before inking or broadening the pencil-lines, so as to make a minimum of erasing and cleaning after the drawing is finished. When drawing pencil-h'nes, the pencil should be held in a lane passing through the edge of the T-square perpen:ular to the plane of the paper and making an angle with le plane of the paper equal to about 60". Lines should always be drawn from left to right. A soft conical-pointed pencil should be used for lettering, figuring, and all free-hand work. T/u- Dra-iSjing-pen, — The best form, in the writer's opinion, is thai shown in Fig. 14. The spring on the upper blade

^ unn*

:ads the blades sufficiently apart to allow for thorough ,ning and sharpening. The hinged blade is therefore unnecessary. The pen should be held in a plane passing through the edge of the T-square at right angles to the plane of the paper, and making an angle with the plane of the paper ranging from 60° to 90°, The best of drawing-pens will in time wear dull on the >int, and until the student has learned from a competent

'O BRA WING AND DESIGNING. teacher how to sharpen his pens it would be better to have them sharpened by the manufacturer. It is difficult to explain the method of sharpening a drawing-pen. If one blade has worn shorter than the other, the blades should be brought together by means of the thumb-screw, and

placing the pen in an upright position draw the point to and fro on the oil-stone in a plane perpendicular to it, raising and lowering the handle of the pen at the same time, to give the proper curve to the point. The Arkansas oil-stones (No. 21 of ** The Complete Outfit ") are best for this purpose. The blades should next be opened slightly, and holding the pen in the right hand in a nearly horizontal position, place the lower blade on the stone and move it quickly to and fro, ulightly turning the pen with the fingers and elevating the h^niUc a little at the end of each stroke. Having ground the lower blade a little, turn the pen completely over and grind the upper blade in a similar manner for about the same length of time; then clean the blades and examine the extreme pv^intH» and if there are still bright spots to be seen continue the ^linilin^ until they entirely disappear, and finish the nhiupenin^ by polishing on a piece of smooth leather. y\w hliules shouUl not be too sharp, or they will cut the \\\w\ , The ^rinilin^j should be continued only as long as the biujht npot!* show on the points of the blades. When inkii\K» the pen should be held in about the same I^ohUivm\ an ih^seribed for holding the pencil. Many draftsU\en hoKI the pen vertically. The position may be varied \^ith ijoo\l ieH\iltH as the pen wears. Lines made with the Mf^ iih\»uld only be drawn from left to right.

INTRODUCTORY INSTRUCTIONS. H THE TRIANGLES. The triangles shown at Fig. 4 (in ** The Complete Outfit ") are 10'' and y" long respectively, and are made of transparent celluloid. The black rubber triangles sometimes used are but very little cheaper (about 10 cents) and soon become dirty when in use ; the rubber is brittle and more easily broken than the celluloid. Angles of 15*, 75*, 30**, 45**, 60**, and 90** can readily be drawn with the triangles and T-square. Lines parallel to oblique lines on the drawing can be drawn with the trianglea by placing the edge representing the height of one of them so as to coincide with the given line, then place the edge representing the hypotenuse of the other against the corresponding edge of the first, and by sliding the upper on the lower when holding the lower firmly with the left hand any number of lines may be drawn parallel to the given line. The methods of drawing perpendicular lines and making angles with other lines within the scope of the triangles andT*

square are so evident that further explanation is unnecessary. THE T-SQUARE. The use of the T-square is very simple, and is accomplished by holding the head firmly with the left hand against the left-hand end of the drawing-board, leaving the right hand free to use the pen or pencil in drawing the required lines. V THE DRAWING-BOAREt If the left-hand edge of the drawing-bcard is straight and the T-square, then horizontal lines parallel to the upper edge of the paper and perpendicular to the left-hand edge may be drawn A^th the T-square, and lines perpendicular to these can be made by means of the triangles, or sei squares, as they are sometimes called.

12 DRAWING AND DESIGNING, THE TRIANGULAR SCALE This scale, illustrated in Fig. 3 (in "The Complete Outfit"), was arranged to suit the needs of the students in machine drawing. It is triangular and made of boxwood. The six tdges are graduated as follows; ^V'' or full size, ^V"* i" and I" = I ft., i'' and i" = i ft., 3'' and li" = i ft., and 4" and 2" = I ft. Drawings of very small objects are generally shown enlarged — e.g., if it is determined to make a drawing twice the full size of an object, then where the object measures one inch the drawing would be made 2", etc. Larger objects or small machine parts are often drawn full size — i.e., the same size as the object really is — and the draw* ing is said to be made to the scale of full size. Large machines and large details are usually made to a reduced scale — e.g., if a drawing is to be made to the scale of 2" = I ft., then 2'' measured by the standard rule would be divided into 12 equal parts and each part would represent l". THE SCALE GUARD. This instrument is shown in No. 17 (in "The Complete

Outfit "). It is employed to prevent the scale from turning, •to that the draftsman can use it without having to look for tee particular edge he needs every time he wants to lay off a measurement THE COMPASSES. When about to draw a circle or an arc of a circle, take liold of the compass at the joint with the thumb and two first fingers, guide the needle-point into the center and set the pencil or pen leg to the required radius, then move the thumb. and forefinger up to the small handle provided at the top of

INTRODUCTORY INSTRUMENTS. 13 the instrument, and beginning at the lowest point draw the line clockwise. The weight of the compass will be the only down pressure required. The sharpening of the lead for the compasses is a very important matter, and cannot be emphasized too much. Before commencing a drawing it pays well to take time to properly sharpen the pencil and the lead for compasses and to keep them always in good condition.

Fig. 16. The directions for sharpening the compass leads are the same as has already been given for the sharpening of the straight-line pencil. THE DIVIDERS OR SPACERS. This instrument should be held in the same manner as de* scribed for the compass. It is very useful in laying off equal distances on straight lines or circles. To divide a given line into any number of equal parts with the dividers, say 12, it is best to divide the line into three or four parts first, say 4, and then when one of these parts has been subdivided accurately into three equal 'parts, it will be a simple matter to step off these latter divisions on the remaining three-fourths of the given line. Care should be taken not to make holes in the paper with the spacers, as it is difficult tb ink over them without blotting. THE SPRING BOWS.

These instruments are valuable for drawing the small circles and arcs of circles. It is very important that all the small arcs, such as fillets, round corners, etc. , should be carefully pencilled in before beginning to ink a drawing. Many

14

DRAWING AND DESIGNING.

good drawing^ are spoiled because of the bad joints between small arcs and straight lines. When commencing to ink a drawing, all small arcs and small circles should be inked first, then the larger arcs and circles, and the straight lines last. This is best, because it is

Fio. 17. nujch easier to know where to stop the arc line, and to draw the straight line tangent to it, than vice versa.

IRREGULAR CURVES. The irregular curve shown in Fig. 5 is useful for drawing iirr^uhir curves through points that have already been found by iHinsi ruction, such as ellipses, cycloids, epicyloids, etc., as in the I UM\s of gear-teeth, cam oudines, rotary pump wheels, etc. When using these curves, that curve should be selected that will coincide with the greatest number of points on the

INTRODUCTORY INSTRUCTIONS. 15 THE PROTRACTOR. This instrument is for measuring and constructing angles. It is shown in Fig. 12. It is used as follows when measuring an angle: Place the lower straight edge on the straight line

nrhich forms one of the sides of the angle, with the nick •exactly on the point of the angle to be measured. Then the number of degrees contained in the angle may be read from the left, clockwise. In constructing an angle, place the nick at the point from ivhich it is desired to draw the angle, and on the outer circumference of the protractor, find the figure corresponding to the number of degrees in the required angle, and mark a point on the paper as close as possible to the figure on the protractor; after removing the protractor, draw a line through this point to the nick, which will give the required angle. SHADE LINES AND SHADING. Shade Lines are quite generally used on engineering working drawings; they give a relieving appearance to the projecting parts, improve the looks of the drawing and make it easier to read, and are quickly and easily applied. The Shading of the curved surfaces of machine parts is sometimes practiced on specially finished drawings, but on working drawings most employers will not allow shading berable to quick printing. So taking everything into con* sideration the system of making working drawings directly on cards and varnishing them is probably the best. It is the system used by the Schenectady Locomotive Works and tnany other large engineering establishments. In size the cards are made 9" X 12", 12" X 18", 18" X 24"; they are made of thick pasteboard mounted with Irish linen recordpaper. The drawings are pencilled and inked on these cards in the usual way, and the sections are tinted with the conven* tional colors, which are much quicker applied than hatchlines. The face of the drawing is protected with two coats of white shellac varnish, while the back of the card is usually given a coat of orange shellac. The white varnish can easily be removed with a little

alcohol, and changes made on the drawing, and when revar* nished it is again ready for the shop. In the hands of an experienced workman a woridilg drawing is intended to convey to him all the

INTRODUCTORY INSTRUCTIONS. I9 information as to shape, size, material, and finish to enable him to properly construct it without any additional instructions. This means that it must have a sufficient num* ber of elevations, sections, and plans to thoroughly explain and describe the object in every particular. And these views should be completely and conveniently dimensioned. The dimensions on the drawing must of course give the sizes to which the object is to be made, without reference to the scale to which it may be drawn. The title of a working drawing should be as brief as possible, and not very large — a neat, plain, free-hand printed letter is best for this purpose. Finished parts are usually indicated by the letter ** f," and ifitisall to be finished, then below the title it is customary to write or print ** finished all over." The number of the drawing may be placed at the upper left-hand corner, and the initials of the draftsman immedi* ately below it. Lettering. — All lettering on mechanical drawings should be plain and legible, but the letters in a title or the figures on a drawing should never be so large as to make them appear more prominent than the drawing itself. The best form of letter for practical use is that which gives the neatest appearance with a maximum of legibility and requires the least amount of time and labor in its construction. Figuring. — Great care should be taken in figuring or dimensioning a mechanical drawing, and especially a working drawing. ^ To have a drawing accurately, legibly, and neatly figured is considered by practical men to be the most important part of a working drawing.

20 DRA WING AND DESIGNING. There should be absolutely no doubt whatever about th< character of a number representing a dimension on a drawing Many mistakes have been made, incurring loss in time labor, and money through a wrong reading of a dimension. Drawings should be so fully dimensioned that there wil be no need for the pattern-maker or machinist to measure anj part of them. Indeed, means are taken to prevent him front doing so, because of the liability of the workman to mata mistakes, so drawings are often made to scales which are dif ficult to measure with a common rule, such as 2" and 4'' = I ft. STANDARD CONVENTIONAL SECTION LINES. Conventional section lines are placed on drawings to distin guish the different kinds of materials used when such drawings are to be finished in pencil, or traced for blue printing, or tc ( : used for a reproduction of any kind. Water-colors are nearly always used for finished drawing! and sometimes for tracings and pencil drawings. The color tints can be applied in much less time than it takes to hatch-line a drawing. So that the color metho< should be used whenever possible. To apply the color tint. — Great care should be taken in d© termining the depth of the tint to be used ; when only th^ section parts are to be colored the tints should be quite ligk because it is much easier to obtain an even wash and a softci and more artistic effect. Before applying the color the drawing board should be cleared of drawing instruments, etc., ac that it may be easily turned to enable the student to keef

INTRODUCTORY INSTRUCTIONS. 21 the bounding color line always to his left, and keeping the brush in such position that the color just touches the bounding line transfer the color to the drawing with long sweeps of the brush until the surface is covered. Press out all color remaining in the brush with the fingers and apply the brush again to the little puddles remaining on the paper. The brush will draw it back into itself and leave an even tint all over the section. Fig. 20. — This figure shows a collection of hatch-lined sections that is now die almost universal practice among

draftsmen in this and other countries, and may be considered standard. No. I. To the right is shown a section of a wall made of rocks. When used without color, as in tracing for printing, the rocks are simply shaded with India ink and a 175 Gillott steel pen. For a colored drawing the ground work is made of gamboge or burnt umber. To the left is the conventional representation of water for tracings. For colored drawings a blended wash of Prussian blue is added. No. 2. Convention for Marble, — When colored, the whole section is made thoroughly wet and each stone is then streaked with Payne's gray. No. 3. Cojivention for Chestnut. — When colored, a ground wash of gamboge with a little crimson lake and burnt umber is used. The colors for graining should be mixed in a separate dish, burnt umber with a little Payne's gray and crimson lake added in equal quantities and made dark enough to form a sufficient contrast to the ground color. No. 4. General Convention for Wood, — When colored the ground work should be made with a light wash of burnt sienna*

DRAWING AND DESIGNING.

INTRODUCTORY INSTRUCTIONS. 23 The graining should be done with a writing-pen and a dark mixture of burnt sienna and a modicum of India ink. p^ No. 5. Convention for Black Walnut. — A mixture of Payne*s gray, burnt umber and crimson lake in equal quantities b used for the ground color. The same mixture is used for grsiining when made dark b)r adding more burnt umber. No. 6. Convention for Hard Pine. — For the ground color make a light wash of crimson lake, burnt umbei, and gamboge, equal parts. For graining use a darker mixture of of crimson lake and burnt umber. No. 7. Convention for Building'Stonc, — The ground tolor is a light wash of Payne's gray and the shade lines are .added mechanically with the drawing-pen or free-hand with the writing-pen. No. 8. Convention^ for Earth, — Ground color, India ink and neutral tint. The irregular lines to be added with a writ-

ing-pen and India ink. No. 9. ^Section Lining for Wrought or Malleable Iron, — When the drawing is Jto be tinted, the color used is Prussian blue. No. 10. Cast Iron. — These section lines should be drawn equidistant, not very far apart and narrower than the body lines of the drawing. The tint is PayneS gray. No. II. Steel, — This section is used for all kinds of steel. The lines should be of the same width as those used for castiron and the spaces between the double and single lines should be uniform. The color tint is Prussian blue with enough crimson lake added to make a warm purple. No. 12. Brass, — This section is generally used for all kinds of composition brass, such as gun-metal, yellow metal.

24 D/^A WING AND DESIGNING. bronze metal, Muntz metal, etc. The width of the full lines, dash lines and spaces should all be uniform. The color tint is a light wash of gamboge. Nos. 23-20. — The section lines and color tints for these numbers are so plainly given in the figure that further instruction would seem to be superfluous. Sometimes draftsmen will Crosshatch all the sectional parts with a uniform space and ilne like that used for cast iron and mark the names of the different materials or their initials in some convenient place on the parts themselves. This does not look as well nor is it any more convenient to experienced men than the other method. CONVENTIONAL LINES. Fig. 21. — There are four kinds: (i) The Hidden Line, — This line should be made of short dashes of uniform length and width, both depending somewhat on the size of the drawing. The width should always be slightly less than the body lines of the drawing, and the

(i>

(4^

Fk;. 21.

lengtli of the dash should never exceed \'' , The spaces between the dashes should all be uniform, quite small, never exceeding y^. This line is always inked in with black ink, {2\ The Line of Motion, — This line is used to indicate point pat lis. The dashes should be made shorter than those of thi' Jiidden line, just a trifle longer than dots. The spaces should of course be short and uniform.

INTRODUCTORY INSTRUCTIONS.

25

(3) Center Lines. — Most drawings of machines and parts of machines are symmetrical about their center lines. When penciling a drawing these lines may be drawn continuous and as fine as possible, but on drawings for reproductions the blackinked line should be a long narrow dash and two short ones alternately. When colored inks are used the center line should be made a continuous red line and as fine as it is possible to make it. (4) Dimension Lines and Line of Sectiofi, — These lines are made in black with a fine long dash and one short dash alternately. In color they should be continuous blue lines. Colored lines should be used wherever feasible, because they are so quickly drawn and when made fine they give the drr.wing a much neater appearance than when the conventional black lines are used. Colored lines should never be broken.

CONVENTIONAL BREAKS.

Fig. 22. — Breaks are used in drawings sometimes to indi« Gate that the thing is actually longer than it is drawn, some*

IS

3BV

11

B

5

Fig. 22.

20 URA WING AND DEStGNtNG. times to show the shape of the cross-section and the kind ^

5.0

.247

12.492

8

f1

5.045

5.5^3

.259

14.564

8

.I

6.o.(M)1

9.688

•344

34.077

8

10. OK)

10.75

.366

40.641

8

USEFUL TABLES AND MISCELLANEOUS INFORMATION. 45 DIFFERENT COLORS OF IRON CAUSED BY HEAT. (Pouillit.) Cm. Fahr. Color. 110* 4iq' , . , . Pale yellow. Mt 430 ... . Dull yellow. Vf> 493 • . . - Crimson. »*' 5021 . . . Violei.purple.anddullblue; betweena6i*a jjo 680 ( and 370* C. u passes 10 bright blue, to sea-

green, and then disappears. 500 933 ... . Commences 10 be covered with a light coatinB of oxide; loses a good deal of ita hardness, becomes much more Impressible to the hammer, and can be twisted with

977 . .

. Becomes nascent red

139a . .

. Sombre red.

147a â– -

. Nascent cherry.

I6S7 . .

. Cherry.

183a . .

. Bright cherry.

aoia . .

. Dull orange.

aiQa . .

. Bright orange.

2373 . .

. White.

»552 . .

. Brilliant white-weld

»73»(. .

. Dazzling white.

TABLE OF DECIMAL EQUIVALENTS OF ONE INCH.

1/64

.015633

.7/64

.265635

33/64

.515625

49/64

.765625

./3a

.03115

9/32

.IS125

17/32

-53'25

.78.25

3/64

.046875

19-64

.296875

35/64

.54687s

.79687s

1/16

.o6a5

S/I6

.3135

9/16

â– 5625

13/18 1

.flias

5/64

.078 H5

21/64

.328125

37/64

.578135

53/64

.82812s

3/31

â– 09375

11/32

â– 34375

K./32

â– 59375

37/32

â– 84375

7/64

- 103375

13/64

â– 359375

39/64

â– 609375

55/64

-85937S

1/8

.125

3/8

â– 375

5/8

.625

7/8

â– 87s

9/64

. 1406J5

15^64

.390625

4>/64

.640625

37/64

.890625

S/3«

.15625

!3/3l

.40625

21/3=

. 65625

39/32

.90635

n/64

.171875

27/64

.421875

43/64

â– 671875

59/64

â– 921875

3/ '6

.1875

7/16

â– 4375

11/16

â– 6875

15/16

-9375

13/64

.ao3"5

29/64

â– 453125

45/64

.70312s

61/64

â– 953125

7/3a

.11875

15/32

.46B75

13/33

â– 71875

31/32

.96875

»S/c>4

â– 234375

31/64

.484375

47/64

â– 734375

63/64

â– 98437s

»/4

.«s

1/3

.50

3/4

â– 75

'1

46

DRAWING AND DESIGNING,

MELTING-POINT OF METALS, ETC.

Names. Pahr. Platinum 3227® Antimony 842 Bismuth 509

Tin 442 Lead .....' 617 Zinc 779 Cast iron 2100

Names. Pahr. Wrought iron ... ... 2900* Steel, hard 2588 Copper 1931 Glass 2012 Beeswax 151 Sulphur 239 Tallow 92

TABLE 5. Weight of Various Substances. Rule. — Divide the specific gravity of the substance by 16 and the quotient will give the weight of a cubic foot of it in pounds.

Substances— Metals.

Aluminum Brass, plate Brass, wire Bronze, gun-metal... Copper, cast Copper, plates

Copper, wire Iron, cast Iron, cast, gun-metal Iron, wrought bars.. Iron, rolled plates...

o2

2.560 8.380 8.214 8.700 8.788 8.698 8.880 7.207 7.308 7.788 7.704

nu v. C

.0926 .3031 .2972 .3147 .3179 .3146 .3212 .2607 .264 .2S17 .2787

Su bstances— Metals.

Lead, cast Lead, rolled Mercury, -{-32" Mercury, 60" Mercury, 212** Steel, plates iSteel, soft 'Steel, wire ! Tin, Cornish, hammered ,Zinc, cast Zinc, rolled

11.352 11,388 13.598 13.580 13.370 7,806 7.833 7.847 7.390 6,861 7.I9I

n^ . a o«-i

.4106 .4119 .4918 .4942 .4836 .2823 •2833 .2838 .2673 .2482 .26

TABLE 6. Weight of Timber ter Cubic Foot.

Ash 46 lbs. Hc

'1^

I:tjn

7/'6

"Uf

1

JO.. 6s

..=7*3

:»^

'/'

Z.I96

S»J

51 B4*

.'a

;;;a

J'^i'

'0.

:i

9va3!

ii.jKs

loX

g::s

â– >-ll-s'

,'u^

.».M

"lA

â– â– .78,

.1.04s

j/a

096

9/>e

â– â– 7*7"

.Ms-

>1.(t«

3/4

4S9

6o..3>

I«/J3

i.Mj,

.^«ag

'l/i

7/8

6I.S6.

i'S

'.963!

.,0680

.J/.<

•■/J.

1.061J

-338'*

6J.6.7

../.6

..lisS

4

...5M

.i.S«

./H

6*7

4S-397

•K-

Vi«

".76a

I..96.

•/*

O&l

.ijse.

1/8

â– 3.J6.

•/I

I5/i'

:!K

V>«

'3-77"

843

.1^.6

â– /4

U-1B6

5/B

,38

71.760

S/.6

13. MB

M.607

3/4

63.

S:S

*l'/'i

rs**?

3/8,

â– S-033

sa;

•.ss

,/.«

â– ^â– 37

.S 466 'S-904

la

3>

416

7B.S40

3'/3«

3^ I4T 1 1 10 09 iS • a 19 €^

w 1 • -- ^

11.8743 11.9164 " ".9583 12.0000 12.0416

5.2048 5.2171 5.2293 5.2415 5.2536

3 i»2 136 3 "76 523 3 241 792 3 307 949 3 375 000

1 2.0830 1 2. 1 244 12.1655 12.2066 12.2474

5.2656 5.2776 5.2896 5.3015 5.3133

USEFUL TABLES AND MKCELLANEOUS INFORMATION. 47*

Number i5»

bquare.

Cube.

Square koot.

Cube Root.

2 28 01

3 442 95'

12.2882

S-325'

152

2 31 04

3 5" 808

12.3288

5.3368

»53

2 34 09

3 581 577

12.3693

5-3485

«54

2 37 16

3 652 264

12.4097

5.3601

'55

2 40 25

3 723 875

12.4499

5-37 '7

156

2 43 36

3 796 4'6

12.4900

5-3832

157

2 46 49

3869893

12.5300

5-3947

158

2 49 64

3 944 3»2

12.5698

5.4061

'59

2 52 81

4 019 679

12.6095

5-4'7S 5.4288

160

2 56 00

4 096 000

12.6491

ibi

2 59 21

4 »73 281

12.6886

5.4401

162

2 62 44

4 251 528

12.7279

5-4514

163

2 65 69

4 330 747

12.7671

5.4626

164

2 68 96

4 410 944

12.8062

5-4737

165

2 72 25

4 492 '25

12.8452

5.4848

166

2 75 56

4 574 296

12.8841

5-4959

167

2 78 89

4 657 463

12.9228

5. 5c 69

168

2 82 24

4 741 632

12.9615

5.5178

169

2 85 61

4 826 809

13.0000

5.5288

170

2 89 00

4 9«3 000

13.0384

5-5397

'7'

2 92 41

5 000 211

13-0767

5-5505

172

2 95 84

5 088 448

1 3. 1 149

5-5613

"73

2 99 29

5 177 7'7

'3-'529

5.5721

174

3 02 76

5 268 024

1 3- '909

5.5828

'75

3 06 25

5 359 375

13.2288

5-5934

170

3 09 76

5 45' 776

13.2665

5.6041

177

3 13 29

5 545 233

'3-3041

5-6147

178

3 '6 84

5 639 752

13-34 1 7

5.6252

'79

3 20 41

5 735 339

'3-379'

5-6357

180

3 24 00

5 832 000

13.4164

5.6462

181

3 27 61

5 929 741

'34536

5-6567

182

3 3' 24

6 028 568

13.4907

5.6671

183

3 34 89

6 128 487

13-5277

56774

184

3 38 56

6 229 504

13-5647

^fv

'85

3 42 25

6 331 625

13-6015

5.6980

186

3 45 96

6 434 856

136382

5-7083

187

3 49 69

6 539 203

136748

5.7185

188

3 53 44

6 644 672

'3-7"3

5-7287

189

3 57 21

6 751 269

13-7477

5-7388

190

3 61 00

6 859 000

13.7840

5-7489

191

3 64 81

6 967 871

13.8203

5-7590

192

36864

7 077 888

13.8564

5-7690

»93

3 72 49

7 '89 057

13.8924

5.7790

,94

3 76 36

7 30' 384

13.9284

5.7890

»95

3 80 25

7 4'4 875

13-9642

5-7989

196

384 16

7 529 536

14.0000

5.8088

'^Z

38809

7 645 373

14.0357

5.8186

198

3 92 04

7 762 392

14.0712

5.8285

'99

3 96 OI

7 880 599

14.1067

5-8383

200

4 00 00

8 000 000

14.1421

5.8480

47

dj:ah'ixg axd designing.

an » 206 21C

H«^

Cube.

Square Root.

Cube Ruot. 1

4 04 01 4 08 04 4 12 09 4 16 16

4 20 25

8 120 601 8 242 408 8 365 427 8 489 664 8 615 125

14.1774 14.2127 14.2478 14.2829 M.3o 76 5 >5 29 5 »9 84 5 24 41 C 2Q 00

11 543 I7 II 697 083 11 852 352 12 008 989 12 167 000

1 5-0333 1 5.0665 15.0997 151327

15.1658

6.0912 6.1002 6. 1 09 1 6.1 180 6.1269 6.1358 6.1446 61534 6.1622 6 1710 6.1797 6.1885 6.1972 6.2058 62145

.•3» 5 33 ^' -3- 5 3S 24 -34 5 47 5

12 326 391 12 487 168 12 649 337 12 Si 2 904 12 977 875

15.1987 15-2315 15.2643 15.2971 153297

.. ;o 5 50 90 .•V^ 5 (>6 44 .\N 5 :» -' -»4v^ ^ 76 00

13 144 256 13 312 053 13 481 272 13 651 919 13 824 000

15-3623 15-3948 15.4272 15.4596 154919

.'41 ^ So 81 i^i S ^^5 64 i\ \ 5 ^>o •49 .•44 ,S 05 36 .it t> 00 i^

13 997 521 14 172 4SS 14 348 907 14 526 784 14 706 125 14 886 936 15 C69 223 IS 252 992 15 438 249 15 625 000

15.5242 15-5563 15.5885 15 6205 15.6525 15.6844 15.7162 1 5.7480

15-7797 15.8114

6.2231 6.2317 6.2403 6.2488 6.2573

-*4^ i47 ^*40

05 16 6 10 o) 6 15 04 6 20 01 6 25 00

6.2638 6.2743 6.2828 6.2912 6.2996

USEFUL TABLES AND MISCELLANEOUS INFORMATION. 47*

Number 251

Square. 6 30 01

Cube.

Square Koot.

Cube Koot. I

15 813 251 16 003 008

15-8430

6.3080 1

252

6 35 04

15-8745

6.3164

253

6 40 09

16 194 277

15.9060

6.3247

254

6 45 16

16 387 064

15.9374 15.9687

6.3330

255

6 50 25

16 s8i 375

6.34n

256

6 55 36

16 777 216

16.0000

6.3496

257

6 60 49

16 974 593

16.0312 16.0024

6.3579

2s8

6 65 64

17 »73 5»2

6.3661

259

6 70 81

>7 373 979

16.0935

6.3743

260

6 76 00

17 576 000

16.1245

6.3825

261

6 81 21

17 779 581

16.IJ55

16.1864

6.3907

262

6 86 44

17 984 728

6.39^8

263

6 91 69

18 191 447

16.2173

6.4070

264

6 96 96

18 399 744

16.2481

6.4 1 51

265

7 02 25

18 609 625 1

16.2788

6.4232

266

7 07 56

18 821 096

16.3095

6.4312

267

7 12 89

19 034 163

16.3401

6.4393

268

7 »8 24

19 248 832

16.3707

6.4473

269

7 23 61

19 465 109

16.4012

6.4553

270

7 29 00

19 683 000

16.4317

6.4633

271

7 34 41

19 902 511

16.4621

6.4713

272

7 39 84

20 123 648

16.4924

6.4792

273

7 45 29

20 346 417

16.5227

6.4872

274

7 50 76

20 570 824

165529 16.5831

6.4951

275 276

7 56 25

20 796 875

6.5030

7 61 76

21 024 576

16.6132

6.5108

277

7 67 29

21 253 933

16.6433

6.5187

278

7 7^ 84

21 484 952

16.6733

6.5265

279

7 78 41

21 717 639

16.7033

6.5343

280

7 84 00

21 952 000

16.7332

6.5421 6.5499

281

7 89 61

22 188 041

16.7631

282

7 95 24

22 425 768

16.7929

6.5577

283

8 00 89

22 665 187

16.8226

6.5654

284

8 06 56

22 906 304

16.8523

$•5731

285

8 12 25

23 M9 «25

16.8819

6.5808

286

8 17 96

23 393 656

16.9115

6.5885

287

8 23 69

23 639 903

16.941 1

6.5962

288

8 29 44

23 887 872

16.9706

66039

289

8 35 21

24 137 569

17.0000

6.6115

290

8 41 00

24 389 000 24 642 171

17.0294

6.6191

291

8 46 81

17.0587 17.0880

6.6267

292

8 52 64

24 897 088

6.6343

293

8 58 49

25 »53 757 25 412 184

17.1172

6.6419

294

8 64 36

17.1464

6.6494

295

8 70 25

25 672 375

17.1756

6.6569

296

8 76 16

25 934 336

17.2047

6.6644

297

8 82 09

26 198 073

17.2337

6.6719

298

8 88 04

26 463 592

17.2627

6.6794

299

8 94 01

26 730 899

17.2916

6.6869

300

9 00 00

27 000 000

17.3205

6.6943

T*

DRAWING AND DESIGNING.

Number

Square.

Cube.

Square Root.

Cube Root.

301

9 06 01

27 270 901

17-3494

6.7018

302

9 12 04

27 7- 5499

6.7533

309

9 54 81

29 503 629

17.5784

6.7606

3*0

9 61 00

29 791 000

17.6068

6.7679

3 832 «39 798 359 140 608 000

22.7156 22.7376 22.7596 22.7816 22.8035

8.0208 8.0260 8.031 1 8.0363 8 0415

27 14 41 27 24 84 27 35 29 27 45 76 27 56 25 27 66 76 27 77 29 27 87 84 27 98 41 :8 09 00 2S 19 61 .\S 30 24 2S 40 89 .'8 51 56 28 (»2 2Q

141 420 761 142 236 648 143 055 667 143 877 824 144 703 125

22.8254 22.8473 22.8692 22.8910 22.9129

8.0466 8.05 1 7 8.0569 8.0620 8.0671

>4S 53' 576 146 363 183 147 197 952 148 035 889 148 877 000

22.9347 22.9565 22.9783 23.0000 23.0217

8.0723 8.0774 8.0825 8.0876 8.0927

149 721 291 150 568 768 151 419 437 152 273 304 »53 130 375 1 53 990 650 »54 854 153 155 720 872 156 590 819 I 57 464 000 158 340 421 159 220 088 160 103 007 160 989 184

161 S78 625 162 771 336 163 667 323 164 5C>6 592 165 469 149 166 375 000

23-0434 23.0651 23.0868 23.1084 23.1301

8.0978 8.1028 8.1079 8. II 30 8.1180

530 .\S 72 96 537 -"^ ^"^3 69 538 1 28 1)4 44 530 29 03 21 ^4v% 21) 10 CH^

23-i5»7 23-1733 23.1948 23.2164 23-2379 .

8.1231 8.1281 8-1332

8.1382 8 »433

51 2 5»3 Ml Ms ,\|v)

.V) 20 81 29 37 o5

36 12 01 36 24 04 36 36 09 36 48 16 36 60 25

217 081 801 218 167 208 219 256 227 220 348 864 221 445 125

24-5" 53 24.5357 24-5561 24-5764 24.5967

8.4390 8.4437 8.4484 8.4530 8.4577

eo6 eo8 609

36 72 36 36 84 49 36 96 64 37 08 81 37 21 00

222 54c 016 223 648 543 224 755 712 225 866 529 226 981 000

24.6171 24.6374 24.6577 24.6779 24.6982

8.4623 8.4670 8.4716 8.4763 8.4809

en 612 613 614 615

37 33 21 37 45 44 37 57 69 37 69 96 37 82 25

228 099 131 229 220 928 230 346 397 231 475 544 232 608 37.;

24.7184 24.7386 24.7588 24.7790 24.7992

8.4856 8.4902 8.4948 8.4994 8.5040

616 617 618 619 620

37 94 56 38 06 89 38 19 24 38 31 6i 38 44 00

233 744 896 234 885 113 236 029 032 237 176 659 238 328 000 239 483 061 240 641 848 241 804 367 242 970 624 244 140 625

24.8193 24.839s 24.8596 248797 24.8998

8.5086 !-5'32 8.5178 8.5224 8.5270

621 622 623 624 625

38 56 41 38 68 84

38 81 29 38 93 76 39 c6 25

24.9199 24.9399 24.9600 24.9800 25.0000

8.5316 8.5362 8.5408 8.5453 8.5499

1 " 626 1 627 1 628 1 629 630

39 18 76 39 31 29 39 43 84 39 56 41 39 69 00 39 ^i 61 39 94 24 40 06 89 40 19 56 40 32 25 40 44 96 40 57 69

40 70 44 40 83 21 40 96 00 41 08 81 41 21 64 41 34 49 41 47 36 41 60 25

245 3»4 376 246 491 883 247 673 152 248 858 189 250 047 000

25.0200 25.0400 25.0599 25.0799 25.0998

8.5544 8.5590 8-5635 8.5681 8.5726

•

031 632 633 634 63s 636 637 638 639

640 641 642 643 644 64 s

251 239 591 252 435 968 253 636 137 254 840 104 256 047 875

25.1197 25.1396 25-1595 25.1794 25.1992

8.5772 8.5817 8.5862 8.5907 8.5952

257 259 456 258 474 853 259 694 072 260 917 119 262 144 000

25.2190 25.2389 25.2587 25.2784

25.2982

8.5997 8.6043 8.6088 8.6132 8.6177

263 374 721 264 609 288 265 847 707 267 089 984 268 336 125

25.3180 25-3377 25-3574 25.3772 25.3969

8.6222 8.6267 8.6312 8.6357 8.6401

646 647 648 649 650

41 73 16 41 86 09 41 99 04 42 12 01 42 2S 00

269 586 136 270 840 023 272 097 792 273 359 549 274 625 000

25.4165 25.4362 25.4558 25-4755 2S49'^'

8.6446 8.6490 8.6535 8.6579 8.6624

WEFUL TABLES AND MISCELLANEOUS INFORMATION, 47

Numberj Square.

Cube.

Square Root.

Cube Root.

651 653 654 655

42 38 01 42 51 04 42 64 09 42 77 16 42 90 25

275 894 451 277 167 808 278 445 077 279 726 264 281 on 375

25-5M7 255343 25-5539 25-5734 25-5930

S.6668 8.6713 8.6757 8.6801 8.6845

656 657 658

43 03 36 43 16 49 43 29 64 43 4a 81 43 56 00

282 300 416 283 593 393 284 890 312 286 191 179 287 496 000

25.6125 25.6320 25.6515 25.6710 25.6905

8.6890 8.6934 8.6978 8.7022 8.7066

661 662 663 664 665

43 69 21 43 82 44 43 95 69 44 08 96 44 22 25

288 804 781 290 117 528 291 434 247 292 754 944

294 079 625

25.7099 25.7294 25.7488 25.7682 25.7876

8.7110 8.7154 8.7198 8.7241 8.7285

666 667 668 669 670

^^ 35 56 44 48 89 44 62 24 44 75 61 44 89 GO

295 408 296 296 740 963 298 077 632 299 418 309 300 763 000

25.8070 25.8263 25-8457 25.8650 25.8844

8.7329 8.7373 8.7416 8.7460 8.7503

671 672 673 674 675

45 02 41 45 «5 84 45 29 29 45 42 76 45 56 25

302 III 711 303 464 448 304 821 217 306 182 024 307 546 875

25-9037 25.9230 25.9422 25.9615 25.9808

8.7547 8.7590 8.7634 8.7677

8.7721

676 677 678 679 680

45 69 76 45 83 29 45 96 84 40 10 41 46 24 00

308 915 776 310 288 733 311 665 752 313 046 839 314 432 000

26.0000 26.0192 26.0384 26.0576 26.0768

8.7764 8.7807 8.7850 8.7893 8.7937

681 682 683 684

68s

46 37 61 46 51 24 46 64 89 46 78 56 46 92 25

315 821 241 317 214 568 318 611 987 320 013 504 321 419 125

26.0960 26.1 151 26.1343 26.1534 26.1725

8.7980 8.8021 8.8066 8.8109 8.8152

686 687 688 689 690

47 05 96 47 19 69 47 33 44 47 47 21 47 61 00

322 828 856 324 242 703

325 660 672 327 082 769 328 509 000

26.1916 26.2107 26.2298 26.2488 26.2679

8.8194 8.8237 8.8280 8.8323 8.8366

691 692 693 694 695

47 74 81 47 88 64 48 02 49 48 16 36 48 30 25

329 939 371 33« 373 888 332 812 5C7 334 25s 384 335 702 375

26.2869 26.3059 26.3249

26.3439 26.3629

8.8408 8.8451 8.8493 8.8536 8.8578

696 697 698 699 700

48 44 16 48 58 09 48 72 04 48 86 01 49 00 00

337 153 536 338 608 873 340 068 392 341 532 099 343 000 000

26.3818 26.4008 26.4197 26.4386 26.4575

8.8621 8.8663 8.8706 8.8748

8.8790

47

15

DRAWING AND DESIGNING.

[Number

Square. Cube. 1 Square Root.

Cube Root.

701 702 703 704 705

49 14 01 49 28 04 49 42 09 49 56 16 49 70 25

344 472 101 345 948 408 347 428 927 348 913 664 350 402 625

26.4764 26.4953 26.5141 26.5330 26.5518

a8833 8.8875 8.8917 8.8959 8.9001

706 707 708 709 710

49 84 36 49 98 49 50 12 64 50 26 81 50 41 00

351 89s 816 353 393 243 354 894 912 356 400 829 357 9»» 000

26.5707 26.5895

26.6083 26.6271 26.6458

8.9043 8.9085 8.9127 8.9169 8.92 II

7i« 712 713 714 715

50 55 21 50 69 44 50 83 69 50 97 96 51 12 25

359 425 431 360 944 128 362 467 097 363 994 344 365 525 875

26.6646 26.6833 26.7021 26.7208 26.7395

8.9253 8.9295

8.9337 8.9378 8.9420

716 717 718 719 720

51 26 56 51 40 89 5« 55 24 51 69 61 51 84 00

367 061 696 368 601 813 370 146 232 371 694 959 373 248 000

26.7582 26.7769 26.7955 26.8142 26.8328

8.9462 8.9503 8.9545 8.9587 8.9628

721 722 723 724 725

51 98 41 52 12 84 52 27 29 52 41 76 52 56 25

374 805 361 376 367 048 377 933 067 379 503 424 381 078 125

26.8514 26.8701 26.8887 26.9072 26.9258

8.9670 8.971 1 8.9752 8.9794 89835

726 727 728 729 730

52 70 76 52 85 29 52 99 84 53 14 41 53 29 00 53 43 61 53 5^ 24 53 72 89 53 87 56 54 02 25 54 16 96 54 3« 69 54 46 44 54 61 21 S4 76 00

382 657 176 26.9444 384 240 583 26.9629 385 828 352 26,9815 387 420 489 27.0000 -^Sq 017 000 27.018;

8.9876 8.9918 8.9959 9.0000 9.0041

73» 732 733 734 735

390 617 891 392 223 168

393 83^ 837 395 446 904 397 06s 375

27.0370 27.0555 27.0740 27.0924 27.1 109

9.0082 9.0123 9.0164 9.0205 9.0246 9.0287 9.0328 9.0369 9.0410 9.0450

736 737 738 739 740

39S 688 256 400 315 553 401 947 272 403 583 419 405 224 000

27.1293 27.1477 27.1662 27.1846 27.2020

741 54 90 81 742 55 05 64 743 55 20 40 744 55 35 3^ 745 55 50 25

406 S69 021 40S 518 4S8 410 172 407 411 830 784 413 493 625

27.2213 27.2397 27.2580 27.2764 27.2947

9.0491 9-0532 9.0572 90613 9.0654

746 747 748 749

55 65 16 55 80 09 55 95 04 56 10 01

56 25 00

415 160 936 27.3130 416 832 723 27.3313 418 508 992 ; 27.3496 420 i8q 749 , 27.3679 421 87:; 000 1 27.3861

9.0694 9-0735 9-0775 9.0816 9.0856

VSEFUl. TABIDS AND MISCELLANEOUS INFORMATION. 47"

Numt«

Squ...,

Cube.

Squ.« Rm.

Cube Root.

7S'

56 40 01

423 %H 75!

27.4044

^0896

75-

56 5504

42s 259 008

»7.42»6

9-0937

7S3

56 70 09

3?^^^

27.4408

9.0977

7S*

568s .6

37-459'

9.1017

7SS

57 00 as

43° 368 875

»7-4773

9..057

7S6

57 '5 3"

432 oSi 116

'7-4955 27.5.3S

9..C98

757

57 30 «

433 798 093

9.1.38

758

S7 4S 64

435 5'9 S'=

27.S3'8

9.1178

J8

57 6081

JPS^S

27.5500

9.12.8

57 7I 00

27.568.

*.25!

57 9' ='

440 7" 081

17.6043

9.1298

76:

S»c6 44

442 450 728

91338

76J

581: 69

444 194 947

27.6225

9.. 378

76+

583696

445 943 744

27.6405

9..4.8

76s

^J?.S'_'5_

447 697 1:5

27.6586

9.M5B

766

Vl%

449 455 "^

27.6767

9.. 498

767

45' ^'7 663

27.6948

9-1537

763

5898^4

45' 984 332

9-. 577

769

59 '3 6'

454 750 ^

27-7308

9,1617

770

S9 )9 00

456 533 000

17-7489 27:7669

9.1657 9.1696

J71

59 44 41

458 3'4 o"

77 =

59 S9 04

46o«,9 648

27.7849

9-.73fi

773

59 75 ^

46. 889 9,7

=7.8029

9-1775

774

59 9=> 70

463 6S4 824

27.8209

9..8.S

775

60 06 i;

465 484 375

17.8388

g.1855

776

60 3 1 76

467 288 576

27.85^8

9-1894

777

60 37 19

469 097 433

27.8747

9-1933

778

605184 60 68 41

470 910 952

27.8927

9-'973

779

472 729 139

27.9106

9.20.2

780

608400

474 55^ wx*

; 7-9285

9.2052

78 1

60996.

476 379 54'

27.9464

9.209.

78J

61 .5 24

478 ^^^ 768

27 .9643

9.2130

783

61 3089

480 048 687

27.9811

9.1.70

7S4

6: 4O 56

481 890 304 483 736 625

28.0000

a.2log

7S5

6, 62 ,5

28.0179

9.2248

786

61 7796

48s 587 656

280357

9.2287

787

61 93 69

487 443 403

28.0535

9.2326

788

6j 0944

489 3°3 872

280713

9- 2365

789

6« .s "

49' '69 069

180891

9.2404

790

62 41 00

493 039 000

281069

9-2443

79'

62 56 81

494 9' 3 671

23.". 247

9.24S2

792

627^64

496 793 088

28.1425

9.2521

793

61 88 49

498 677 JS7

28.1603

9.1560

794

63 04 36

500 566 I 84

28.I780

9.2599

79S

63 JO 25

502 459 S? 5

2B..9S7

9-2638

-^

63 36 .6

V". 358 336 506 261 573

28.21 3S

9.2677

I'il

63 52 09

2823.2

9.27.6

798

636804

508 169 592

28. 2 489

9- =7 54

799

63 84 0.

510 08= 399

28.2666

9-2793

800

6* 00 00

Sij 000 000

28.2843

9-2832

47"

DttAIViyC AND DBSJCmtrG.

Numbe-

Square.

Cube.

Square koot.

Cube Root

80 1 802 803

804 80s

64 16 01 64 32 04 64 48 09 64 64 16 64 80 25

513 02a 401 515 849 608 S17 781 637 519 718 464 521 660 125

28.5019 a8.3i96 28.3373 28.3549 28.3725

9.2870 9.2900 9.2948 9.2986 9-3025

806 807 808 809 810

64 96 36 65 12 49 65 28 64 65 44 8i

65 61 CO

523 606 616 525 557 943 527 514 112 529 47S 129 531 44( 000

28.3901 28.4077 28.4253 28.4429 28.4605

9-3063 9.3102 9-3»40 9-3 « 79 9-3217

81X 812 814 8.5

65 77 21 65 93 44 66 09 69 66 25 96 66 42 25

533 4" 73« 535 387 328 537 367 797 539 353 144 541 343 375

28.4781 28.4956 28.513a ^!-5327 28.5482

9^3255 9-3294 9-333* 9-3370 9-3408

816 817 818 819 820

66 58 56 667489 66 91 24 67 07 61 67 24 00

543 338 496 545 338 S»3 547 343 43« 549 353 259 551 368 000

28.5657 28.5832 28.6007 28.6182 28.6356

9-3447 9-3485 9-3523 9-3561 9-3599

821 823 824 825

67 40 41 67 56 84 67 73 29 67 89 76 68 06 25

553 387 661 555 412 248 557 441 767 559 476 224 561 515 625

286531 28.6705 28.6880 287054 28.7228

9-3637 9^3675 9^3713 9-3751 9-3789

826 827

828 829 830

68 22 76 68 39 29 68 5584 68 72 41 68 89 00 69 05 6t 69 22 24 69 3$ 89 69 55 56 69 72 25 69 88 96 70 05 69 70 22 44 70 39 21 70 56 00

563 559 976 565 609 283 567 663 552 569 722 789 571 787 000

28.7402 28.7576 28.7750 28.7924 28.8097

93827 9-3865 9-3902 9-3940 9-3978 9.4016

9-4053 9.4091 9.4129 9.4166

832 833 834 83s

573 856 191 575 930 368 578 009 537 580 093 704 582 182 875

28.8271 28.8444 28.8617 28.8791 28.8964

836 837 838 839 840

584 277 056 586 376 253 588 480 472 590 589 719 592 704 000

28.9137 28.9310 28.9482 28.9655 28.9828

9-4204 9-4241 9.4279 9.4316 9-4354

841 842 843 844 845

70 72 81 70 89 64 71 oiS 49 71 23 36 71 40 2«;

594 823 321 596 947 688 599 077 107 601 211 584 603 351 125 ^5 495 736 607 645 423 609 8co 192 6 1 1 960 049 614 125 000

29.0000 29.0172 29-0345 29.0517 29.0689

9-439» 9-4429 9.4466 9-4503 9-4541

846 847 848 849 850

71 57 10 71 74 09 71 91 04 72 08 01 72 25 00

29.0861 29- 1033 29.1204 29. 1 376 29.1548

9-4578 9-4615 9-4652 9.4690 9-4727

USEFUL TABLES, AND MISCELLANEOUS INFORMATION. 47"

«"-'"

S-l-r^.

Cube.

>q.u... H..O.

Lute K«r,

«S'

7* 4* ot

616 J9S 051

39.1719

9-4764

Sjj

7a S9 04

618 470 208

29.1890

9.4BOI

853

72 7609

610 650 477

9.4838

V'"

72 93 16

6j» 83s ii64

'9-"33

9-4875

_85S_ 856

73 'â– > 25

615 026 375

29.2404

9.49.2

73 '7 36

627 222 C16

29-2575

94949

8S7

73 44 49

6*9 42J 793

29.2746

94986

8s8

7361 64

631 628 77 918 919 920

83 90 56 84 08 89 84 27 24 84 45 61 84 64 00

768 575 296

771 095 213 773 620 632 776 151 559 778 688 000

30.265 s 3a2820 30.2985 30.3150 30.33^5

9.7118 9-7153 9.7188 9.7224 9-7259

921 922 923 924 9-5

84 82 41 85 00 84 85 19 29 85 37 76 85 56 25

781 229 9C1 783 777 448 786 ;530 467 788 889 024 791 453 »2S

30.3480

30.3645 30.3809 30.3974 30.4138

9-7294 9.7329 9.7364 9-7400 9-7435

926 9-'7 928 920

85 74 76 85 93 29 86 II 84 86 30 41 86 49 00

794 022 776 796 597 983 799 178 752 801 765 089 804 357 000

30.4302 30.4467 30.4631 30.4795 30.4959

97470 9-7505 9.7540 9.7575

9.7610

^^\\ , 86 67 61 i)32 ! 86 86 24 033 87 04 89 93» 87 23 56 035 87 42 25

806 954 491 809 557 568 812 166 237 814 780 504 817 400 375

30.5 « 23 30.5287 30.5450 30.5614 30.5778

9.7645 9.7680 9.7715 9.7750 9-7785

1) \o 87 60 96 q\7 87 79 69 ^8 87 98 44 gV) i 88 17 21 K^\K^ \ 88 -56 00

820 025 856 822 656 953 825 293 672 827 936 019 830 584 000

30.5941 30.6105 30.6268

30.6431 30.6594

9.7819 9-7854 9.7889 9.7924 9-7959

041 »>4J 041 OK

88 54 81 88 73 64 88 92 49 89 II 36 89 30 2S 89 49 »^ 89 68 09 89 87 04 90 06 01 90 25 00

833 237 62c 835 896 888 838 561 807 841 232 384 843 908 625

30.6757 30.6920 30.7083 30.7246 30.7409

9-7993 9.8028 9.8063 9.8097 9.8132

04^ 047 04H gSO

846 590 536 849 278 123 851 971 392 854 670 349 857 375 000

30.7571 30.7734 30.7896 30.8058 30.8221

9.8167 9.8201 9.8236 9.8270 9.8305

USEFUL TABLES AND MISCELLANEOUS INFORMATION. 47

3f

Number

Square.

Cube.

Square Root.

Cube Root.

95» 952 953 954 955

90 44 01 90 63 04 90 83 09 91 01 16 91 20 25

860 085 351 862 801 408 865 523 177 868 2

OH

onw

.N

J

IP.

'A all

Iv

_a,/3a

31/3"

'1^

'i

'(^

•A

1

il

3A

1 3!

i«

|j|

"?*

>lt

4A

â– i

â– 11

iH

3

3K

3«

-i 3K

m

?!

aV aM

;?(

»X

i%

4ll

6

aV

a,'.

•»

!M

m

'ft

'»

3X

5

StI

7,V

3X

aji

ali

?S

iS

^fi

ill

SK

11!

l\\

'X

7A

â– li

4

3A

311

4X

'H

i

â– ^

3X

3 In cn>ss>section and passes Into a correspond* ^r shaped hole in the connected piece. The diameter of the »crew is rqw.il to the square body. »T— «^y. ij. Piaw an ELKVATioN of a hook-bolt, fasten1^ k piece to a flanged beam, as shown in Fig. 52, and VlAW of tfM boh only, looking down on the bolt head. Scalt

SCJ^EIVS, NUTS, AND BOLTS. 77 Tapered Bolts are used to facilitate fitting where it is necessary that the bolt should be a perfect fit in the hole. Fig. 53 shows a tapered bolt that is in common use in the couplings of propeller-shafts of steamships. As couplingbolts have only to resist the shearing force, caused by the twisting strain on the shaft, the diameter of the bolt is I

4

Fig. 53. the diameter on the line where the two flanges come toftiP

gether, and its strength is equal to f,, 4 As the screwed part of the bolt has only to resist the tension due to screwing up, this part is made smaller in diameter than the small end of the tapered part. In practice, the diameter of the screwed part is generally 7rf+ I made equal to , and the height of the nut from J" to J" less than the diameter of the screw. The advantages gained by using tapered instead of parallel bolts for couplings are: they can be made a perfect fit in the hole, which insures that the different lengths of shaft are in better alignment, are easier withdrawn, and, owing to the diameter of the screw being much smaller than the diam* eter at the junction of the shafts (i.e., the effective diameter), the flanges can be made smaller. Exercise 13. — Draw a tapered bolt for a marine shaft-

78 DRA WING AND DESIGNING. coupling, showing a part of the shaft-flanges» to the dimensions given in Fig. 53. Scale half size i, Construction, — Draw the centre line of the bolt, then the line showing the junction of the flanges, and on this line mark off the diameter of the bolt. From the point (a) draw the line ab 12 inches long and parallel to the axis of the bolt, and from b draw be perpendicular' to ab and -f^" long, join ac which makes the required taper. The radius' (r) is equal to the diameter of the bolt at the large end. Exercise 14. — Draw a tapered bolt as in the preceding exercise, leaving off the parts of the shafts, and making the diameter of the bolt 3 inches, and the. length of the body equal to 8 inches. Scale Jialf size. Foundation-bolts. — This class of bolts is employed for fastening engine- and machine-frames to stone, brick« or concrete foundations. The Rag-bolt (Fig. 54). — This form of bolt is fastened to stone by cutting a Lewis hole, which increases in size as

it descends. The small end of the hole is made from J" to \" larger than the large end of the bolt-head. After the bolt-head is placed in the hole, the space between it and the sides of the hole is filled with molten lead or sulphur, thus securing the bolt firmly in position. The fra^me is cast with a projecting foot through which a hole is cored. This foot passes over the foundation-bolt and the engine- or machineframe is held in position by the pressure of the nut. The diameter of the hole through the foot is = ^/ -j" i"- The diameter of the washer iv is equal to 2rf+ J", and the thickness ^ of d. The distance ^j: is = half the diameter of the washer -j- !"• The section of the bolt-head is oblong and

80 DRAIVIXG AXD DESIGNING, purposely made rough and jagged, which obviously increases the resistance the bolt offers against being withdrawn from the hole. The length L of the head (A) is usually made equal to 6«/and has a taper = ij" per foot. Exercise 15 — Draw a rag-bolt in elevation and plan with a part of a cast-iron engine-frame as shown in Fig. 54, making (1/ » = ij' in diameter. Scale full size. Construction, — Draw the centre line and the line representing the top of the stone foundation, then mark off to (b) the distance which the beginning of the head is below the level of the top of the foundation, and from the point ip) find the taper on one side of the axis in the same manner as in Exercise 13. Make the top of the hole de ^" greater than the large end of the bolt-head, and through (/) draw a line parallel to the side of the bolt-head bc^ which will represent the edge of the hole. To complete the other side of the bolt-head mark off with the dividers equal distances on the other side of the centre line. The Lewis Bolt, shown in Fi^;. 55, is used, in some cases, in preference to the rag-bolt, because it can be much more easilv removed, which is accomplished by withdrawing the key K. The side be of the bolt-head (//) has a taper of 1 j' per foot, while the opposite side is parallel to the axis of the holt. The length L of the head may be made as in tlir design of the rag-bolt, equal to Cxi, In iMg. 55, the bolt is shown holding down the pedestal sliown in Fig. 54, page 79. The hole that the bolt passes thiou'di is rectangular, to allow the pedestal to move l.it

a = area of exposed surface in square inches; / = the pressure per square inch; ;/ = the number of bolts; /f =â– the strain per square inch; Unwin's formula for cylinder-bolts or studs is

^' = \/[-.V^- ('4)

SCREIVS, NUTS, AND BOLTS.

9Jf

D = the diameter of the cylinder; / = the pressure per square inch ; n = the number of bolts. f = the strain per square inch = 2000 lbs. when the diameter of the cylinder is lo"' or less, and 4000 lbs. when above. Cylinder-cover and steam-chest cover-bolts should be of soft steel. Bolts of Uniform Strength. — When a bolt in tension is subjected to irregular strains and heavy vibrations, it is made lighter and stronger by making the area of the cross-section of the unscrewed part equal to that of the screwed part at the bottom of the threads. This is obtained by turning down the bolt-body to the same diameter as the screwed part at the bottom of the threads, leaving a part at each end to fit the hole, as shown in Fig. 60.

FiO. 60. Another method adopted where it is necessary that the bolt should fill the hole it is fitted into, is to drill a hole through the centre of the bolt from the head up to where the screw ends, as shown in Fig. 61. The diameter of the hole is found by the formula

rf, = ^d' - d:.

(I5>

92

DRA WING AND DESIGNING.

where d. = diameter of the bolt ; d = outside diameter of the bolt-body; d^ = the diameter at the bottom of the thread*

f'

Fio. 6x« Nut-locking Devices. — ^The pitch of the threads on screw fastenings is such that nuts subjected to constant pressure will not slack back because of the frictional holding power between the threads of the nut and those of the bolt com* bined with the friction between the bearing-surface of the nut and the piece it is fastening. If, however, the pressure is intermittent and there is much vibration, the nut will slack back when the load on it has been sufficiently reduced to allow the vibrations to overcome the friction which opposes the turning of the nut. Consequently, wherever a scre\f is subjected to much vibration and a varying load, the nut will gradually slack back and allow the connection to work loose unless some locking device is used to keep the nut from rotating backward. A Jam-nut is the simplest and most frequently employed device. This is simply a second nut N (Fig. 62) screwed down on the top of the lower nut L as tightly as possible, and the lower nut turned back to cause the threads in the nut N to press upon the under side of the threads on the bolt, while the threads in the nut L press upon the upper

J

SCREWS, ATUrS. AND BOLTS.

93

side o[ the bolt-threads. Hence all slack between the threads of the bolt and those of the nuts is taken up and the nuts will have a frictional holding power independent of the

tension on the bolt. By this arrangement the load on the bolt is carried on the upper nut, which should be the larger. In practice, however, the thin nut is often put on the top because when screwed down first it requires a special spanner to turn it without disturbing the upper nut, the ordinary spanner or wrench being too thick. The general rule is to make the thin nut equal to half the diameter of the bolt, but many engineers use two ordinary nuts, thus making the height of the nuts equal to twice the diameter of the screw. Others again make a compromise between these methods and make the height of each nut equal to \ of the screw diameter. We recommend the latter method and have used these proportions wherever jam^nuts are shown. This method of

JD/tA WIIfG AND DESIGIfl»G.

locking is too cumbersome to be used oa Uige-sixed nuts. It is rarely employed on nuti over i^" in diameter. SprinGf-washer Nut-lock. — Thii con^ts of a nngle coil of a steel spring, NL, Fig. 63, which keeps the nut J/ from

mr

slacking back, by its elasticity, when the tension on the bolt is reduced. It is employed quite extensively in railwayengineering practice for securing nuts subjected to the heavy vibrations common to this class of work. The form shown in I'ig. 63 is that made by the American Brake Beam Co., and is employed to secure the nuts on the bogie frames, etc., manufactured by tliem. In the cross-section the top of the washer is inclined -^^ of an inch, and when the nut is screwed home its under side conforms to the part of the washer in contact with it. The following proportions agree approximately with the washers manufkctured by the afore-mentioned

company: The outside diameter = /"the distance across the flats of the nut + Vr".

SCX£IVS, UUTS, AND BOLTS. 95 The inside diameter = d the diameter of the bolt -\- \". The mean thickness / is equal to the width w. Exercise i8 — Draw an elevation of a spring-washer nutlock before the nut is screwed down, as shown in Fig. 63. Make d = i" diameter. Scaie twice full sise. Wiles's Nut-lock, shown in Fig. 64, is an ordinary nut sawn half way across. After the nut is screwed home the

u

Fig. 64.

opening is partly closed by the screw S, which causes the threads in the upper part of the nut to clamp the corresponding threads of the bolt. The thickness t of the clamping

96 DRA IV/A'C AND DESIGNING. part of the nut may be made equal to twice the pitch of the Fd threads. The diameter of the screw S = ~, where 22 A= distance across the flat sides of the nut, and late : ^/ :3: nominal diameter of screw; /." iltstance across the flats — \"\

SCRBIVS, NUTS, AND BOLTS.

I04 DRAWING AND DESIGNING. t = thickness of standard nut having the same number of threads per inch ; H •=• d •\' thickness of locking-plate ; r= .09//+ .7. The size of the pipe-tap is = \d^ but need not exceed f" pipe-tap. The projection on the under side of the nut = 7"+ ^V" ^^ allow the nut to bear upon the piston. W^= twice the diameter of the tapped hole at the small end. Exercise 22. — Draw the nut-lockihg arrangement shown in Fig. 68, showing part of the piston and piston-rod. Make ^= 3" and having 5 threads per inch. Scale full size. Construction. — To find the distance across the flats of the hexagon turn to Table 8, page 68, and find the thickness of a nut having 5 threads per inch by subtracting the radius of the screw from half the distance across the flats. To find the diameter of the tapped hole at the small end, turn to the table of Wrought-iron Pipes on page 57. The size of the actual outside diameter is the diameter of the tapped hole at the large end, and the hole is ^" less in diameter for every \" of its length. Complete the drawing, substituting the dimensions in inches for the reference letters, and give the number of threads per inch on the piston-rod screw and the nominal diameter of the pipe-tap. Pin and Pin-joints. — Pins connect pieces by their resistance to shearing at one or two cross-sections. Split Pins, when made of a uniform diameter from ¥nre of a semicircular cross-section and provided with a head, as in Fig. 69, are used for preventing pieces from sepa* rating, while allowing a slight motion in the direction of the axis of the piece that they pass through, as in Fig, 67,

SCHEIVS, NUTS, AND BOLTS.

105

The method of drawing split pins is clearly shown in Fig. 69. The diameter of the pin, in proportion to the diameter d of

Fio. 6^ the piece it passes through, may be = .05^ -|" *^i» taking the nearest size in rf^". Taper Pins» shown in Fig. 70, are used for securing one piece to another in a fixed position, as shown in Fig. 71.

Fig. 70.

They are sometimes split at the small end, and opened out in the same manner as the ordinary sph't pin, to prevent slacking back. The diameter of the tapere\l pin at the large end, in proportion to the diameter {d) of the piece through which it passes, may be made = .06^ -|- .13 and taking the nearest size from Table lo.

io6

UtA WING AND DESiCNING. -

TABLE ICL STAXDAKD STBKL TAPSft-PIHS. Taper one-qnarter inch to the foot.

N-bT ! o

Dlameier at ( Urge end I

A|>proxittwte 1 fractional > siiet) Longest limit ( of length I*

.156 5/3a

172 .193 .219.250 .289

11/64

3/16 7/3ai X ii«/64

i}i iX

2 I aX

6

7

8

9 .591

•341

.409.492

11/32

13/38

X

19/32

3X

3H

4X

sX*

2^

A Knuckle-joint is a pin-joint used for connecting rods in such a manner that one of them will have a rota

Fig. 71.

Fig. 72.

f not Ion in one plane. The connection is made, as shown in V\\[, 71, by the pin P passing through the fork, or double ryr, formed on the rod /?, and the single eye, on the rod R\

f.- *-

SCREWS. NUTS, AND BO/.TS.

107

which fits into the fork. The parts of the rods near the eye and fork arc either left square or have the corners taken ofl for a distance, which makes a part of the rod octagonal in cross-section. In the arrangement shown in Fig. 71, the pin P is allowed to turn and is kept in place by the collar C, which is secured to the turntny-pin /' bj' driving a taper-pin through it and the collar. The width If of the collar should not be less than 2^ tinnes the diameter of the taper-pin. Another method in common use for holding the turningpin in place is to use a loose washer (fl') and split pin, as shown in Fig. 72. In Fig. 73, the pin J' is held against

£^

Fig. 73. turning by a taper-pin /> driven transversely through one of the eyes on the rod R and partly into the pin P. By this airangement all the wear, due to the turning motion, is on the eye of the rod X', which 15 fitted with a steel or bronze

I08 DRAWING AND DESIGNING. The Proportions given in Figs. 72 and 73 make joint stronger than the solid rod. This is necessary to a for bending stresses produced when the pin becomes w Unit 0/ proportions d. Exercise 23. — Draw a plan, elevation, and end v of the joint shown in Fig. 71, showing the method of hoh the pin in place by means of a split pin and washer. &! ^ = I '' Scale full size, I Exercise 24. — Draw a plan partly in section, an ELI

TION and SECTIONAL END VIEW (the plane of section pas through the rod at the line ab) of the knuckle joint show Fig. 73, Make^=ii". Scale full size.

'J

1

â– I

CHAPTER II. KEYS, COTTERS, AND GIBS. Keys are employed to connect wheels, cranks, cams, etc., to shafting transmitting motion by rotation. They are generally made of wrought iron or steel, and are commonly rectangular, square, or round in cross-section. The form of key in general use is made slightly tapered and fits accurately into the key-way, offering a frictional holding power against the keyed piece moving along the shaft. The groove or part where the key fits on the shaft, and the groove into which it fits on the piece it is holding is called the key-bed, keyway or key-seat. For square or rectangular keys, when the keyed piece is stationary on the shaft, the bottom of the groove on the shaft is parallel to the axis, while that of the groove in the piece it is securing is deeper at the one end than the other to accommodate the taper of the key. Keys may be divided into three classes: i. Concave or saddle key; 2. flat key; 3. sunk key. Saddle Key. — This form of key has parallel sides, but is slightly tapered in thickness and is concaved on the under side to suit the shaft, as shown in Fig. 74. As the holding power depends entirely upon the frictional resistance, due to the pressure of the key on the shaft, the saddle key is only 109

110 DRAWING AND DESIGNING. adapted for securing pieces subjected to a light strain. When this key is used for securing a piece permanently, the taper is

usually made i in 96, but when employed on a piece requiring to be adjusted, such as an eccentric, the taper is increased to I in 64 to allow the key to be more easily loosened.

Fir,. 74.

Fic. 75.

Fiat Key. — This form of key. Fig, 75, dlfTers from the saddle key in that it rests on a flat surface filed upon the shaft. It makes a fairly eflicient fastening, but as it drives by resisting the turning of the shaft under it, there is a tendency to burst the kcyed-on piece.

TABLE 11.

■,.„„■.. .»

/

S/16 !.'16

6

9/16

t

Sunk Keys are so called because they are sunk into the shaft and the keyedon piece. Fig. 76, which entirety pre* vt-nts slipping. For engine construction they are usually rectangular in cross-section and made to fit the key-seat oa all sides When subjected to strains suddenly applied, and

KEYS, COTTERS, AND GIBS.

in one direction, th«y are placed to drive as a strut, diagonally, as in Fig. 77.

The following table, taken from Kichards's " Machine Construction," agrees approximately with average practice:

DIMENSIONS C

K SUNK KEYS.

D1

iV

iK

iV

,

I«

3>i\ 4

6

R

B%

â– i/ife

M

7/16

M

H

H

?S 1 I

iH

ltd

^%

IV

T in^

3/.6

%

9/3»

5/ 10

y»

7/16

« 1 «

n/.6

13/16

h

In mill-work, for fastening pulleys, gear-wheels, coup, lings, etc., to shafting they are made slightly greater in depth

112

DKAIVIXG AND DESIGNING,

than breadth. For machine tools they arc generally square in cross-section. The following table gives the sizes of keys used by Wm. Sellers & Co. both for shafting and machine

tools:

TABLE 13.

II

II

II

II

ft

II

ff

n

D

I'A

^H

2

2X

2;^

2H

3

3)4

B

5/16

5/16

7/16

7/16

9/16

II/I6

11/16

11/16

T

H

H

Yz

Yz

}i

H

H

«

n

3^ 11/16 H

//

D

4

B

13/16

7'

'A 1

41-2 I 5 13/16 ' 13/16 "A 'A

15/16 I

6 15 16 I

II

15/16 I

7

ii'«

//

n

7.-4

8

'iV

H^

\yi

i>i

Round Keys. — Taper-pins (Fig. 78) are sometimes used as keys to prevent rotation where a crank or wheel is shrunk on to the end of a shaft or axle. Round keys are used in such a case because of the ease in forming the key-way, which is simply a tapered round hole drilled half into the shaft and half into the shrunk-on piece. The standard proportions of the pins are given on page 106. The size at the large end nearest to ^ of the shaft diameter may be used for this purpose. Fixed Keys are used when it is undesirable to cut a long key-way on the shaft to allow the key to be driven into place after the keyed-on piece is in position. The fixed key is sunk into the shaft, as in Fig. 79, and the keyed-on piece is driven into position after the key is in place. When a keyed-on piece has to be adjusted to different positions on the shaft* to avoid the trouble of drawing a tight key in and out. it is made to slide in the key-way, and the keyedon piece is held against moving along the shaft by means of set-screws, as shown in Fig. 80. 1

K£Y^, COTTERS, AND GIBS,

"3

Fig. 79. Fig. 80. Sliding Feather Key. — This system of keying; secures the piece to the shaft, to transmit motion of rotation, and at the same time allows the keyed-on piece to move along the

Fig. 81. Fn;. ^2. shaft. They may be secured to the keyed piece and slide in

a groove on the shaft, as in Fi^. 81, or secured to the shaft and slide in the f^roove in the keyed piece, as in Fi^. 79. T!ie dimensions for this form of kev mav be taken from Table 13. WoodruflF Keys. — This system of keyinj^ (Fi^cj. 82^7) is used for machine tools, or wherever accurate work is of fir^^t importance. With this form of key, as the key ri^j^hts itstif to the groove in the keyed-on piece, there is no danger of

DRAWING AND DESIGNING.

the work being thrown out of true by badly fitted keys, and, being deep in the shaft, it cannot turn in the key-seat.

Key-beads. — When the point of a key cannot be conveniently reached for the purpose of driving it out, a head is formed on one end, as shown in Fig. 76. Which shows the proportions and method of construction given in RiCHARDS's '■Machine Construction. " 5treDg:th of Keys. — The driving power of saddle keys or keys on (lats cannot be calculated with any degree of accuracy. They are used only where the power transmitted by the keyed on piece is small. Sunk Keys are .subjected to shearing and crushing strains, and are required (1) to transmit the whole of the power transmitted by the shaft, as in crank-shaft couplings, etc., or (2> only a part of the power transmitted by the shaft, as when fastening pulleys, eccentrics, etc. As a general rule, however, all keys arc proportioned to suit the first conditions, unless where the amount of power transmitted by the shaft is exceedingly great in comparison with that taken off at the kcyed-on piece. Let B — breadth of key; /, = length of key; — = radius at which key offers a resistance;

A'EYS, COTTERS, AND GIBS. 115 the shearing of the material which is = 9000

for wrought iron and 11,000 for steel. • 1 90^/y^ = modulus of the section of shaft for torsion = 1720^' for wrought-iron and 2182^' for steel shafts; R = the radius of arm through which P^ the power, is transmitted. Under the first conditions the strength of a tight key would be found by the formula f.Bd = .i^dy. (16) and under the second conditions by the formula f.Bd=PR (17) In the system of sliding keys the crushing action pn the key is greater than when the key is a tight fit in the key-way, and keys of this type should be proportioned to have the moment of shaft torsion = the moment of key shearing = moment of key crushing. Then d TLd .ig6dV,^f,BL-=/~^, . . . (18) and if we takey^ = 2^^, then T ^ B. In practice, however, B is generally greater than T. Length of Key. — From the foregoing formulae it will be seen that the strength of the key is directly proportional to {L) the length. To find the length L when the full power of

ii8

DRAWING AND DESIGNING.

them in position the taper 'should not be more than i in 24^ (J" per foot), but where special means are employed for' holding the cotter against slacking, the taper may be madesr as great as i in 6 (2" per foot).

Forms and Proportions of Cotter-joints. — ^When the fastening is subjected to tension only, the arrangement shown in Fig. 84 is used for securing two pieces together by_ means of a cotter. Fig. 83 shows a method of fastening two rods, R and R\ together to resist thrust and tension. The joint is made by fitting the end of the rod R into a socket 5 formed on the end of the rod R\ and through the socket and rod end driving a cotter until the collar C bears against the socket end. As a cotter-joint is proportioned to withstand the greatestlongitudinal force transmitted by the rod, all parts will therefore be proportional to the diameter d^ of the rod, unless where the dimensions of the rod are increased to insure stiflfness. The following proportions are in accordance with good practice: b, breadth of cotter = 1.3^,; /, thickness of cotter = .3^,; //, diameter of pierced rod = 1.2^,; D, diameter of socket in front of cotter = 2.4^, or 2d. D^ , diameter of socket behind cotter = 2^, ; /?, , diameter of collar on rod 7? = 1.5^,; A thickness of collar on rod R = \d^\ /, the length of the rod and socket beyond the cotter = from Id, to d,.

KB vs. COTTE/IS, AND GIBS.

"7

holes of a diameter equal to the thickness of the cotter and cutting out the metal between them. Again, this form of cotter-way does not weaken the cottered pieces to quite the same extent as when the corners are left sharp. The cotters, however, are not so easily fitted into cotter-ways with round ends, and for that; reason some engineers maku the cotters of rectangular cross-section, fitted into corresponding cotter, ways.

Fig, 83.

Taper of Cotters. — When cotters are employed as a means of adjusting the length of the connected pieces, or for drawing them together, they are made tapcretl in width, as fn Fig. 83, but when used as a holding-piece only, the sides are parallel, as in Fig, ^6. When tapered cotters depend upon tlie friction between their bearing-surfaces for retaining

u

n

^ -, ~i ]

'\:

•^?:

I20 DRAWING AND DESIGNING. rod-end may be made from J" to i" per foot of length, from I in 12 to i in 24. The diameter d on the tapered end is taken, when the cotter-way is curved at the where the curve begins, as in Fig. 84, and at the end cotter-way when the cotter-way is rectangular. Exercise 25. — Draw a sectional elevation, a 1 PLAN, and HALF SECTIONAL PLAN of the cottcr-joint si in Fig. 83. Make d = 2". Scale full size. Exercise 26. — Design cotter-joints suitable for fasten steel piston-rod to the piston and cross-head, as sho>* Figs. 84 and 85. Make the diameter of the rod d^ = 2f' assume that the rod is subjected to a load of 9000 lbs. rod-ends having a taper of i in 12. Scale full she.

Construction. — Having determined the diameter (rf) rod suitable for resisting tensile stresses, then from d fine other proportions of the joints, as in Exercise 25. Me; off the distances / and b along the centre line and mark 0I diameter {li) at the proper point according to the sha] the cotter in cross-section, then in the manner given i construction in connection with Exercise 13 draw the end to the given taper. The construction for fii the taper need not be inked in. Complete the dra^ filling in the actual dimensions and leaving off all rcfe letters. COTTER AND GIB. When one of the pieces connected by the cott a thin straj), as in Fig. "^C), a second cotter, call gib, is used. The gib is provided with a 'head at ends which project over the strap 5, thus prevent!

KEYS, C07TEKS. AND CI3S. 121 |ttie strap) from being forced open by the friction between it and the cotter as the latter is driven into place. Figs. 86 and §9 show the application of gib and cotter to strap-end connecting-rods, where R is the rod and .S the strap. When two gibs are used, as in Fig. 88, the sliding surface on each side of the cotter is the same. Instead o( having both gibs tapered, as shown in Fig. S8, one of them may be parallel and the taper all on one side of the cotter. The strength of the gib and cotter in combination is made the same as the

single cotter and should be proportional to the strap 5. The working strength of the strap at the thinnest part is found by the equation

2^577, = P. T

25/, \

(20)

wfaere/'is the maximum pull on the rr-^, T'the thickness.

>T2)--T-1

I?2 DRAWING AND DESIGNING. and B the breadth of the strap. Then as the gib and cotttf are to have the same strength as the single cotter, and as B is equal to, or a little greater than d (the diameter of therijd)' / may be made equal to .25^ and

\ *='-V^'

7*» the thickness of the strap where it is pierced by the cot*:d> should not be less than 1.3?", /', the distance from the g>^ to the end of the strap, = 2T. I, the distance from the cotter to the end of the rod, = 1,5 7". c, the clearance, shoiiltl not be less than c' (the difference between the widest part of the cotter and the width of the cotter at the top of the gibhead). The method of constructing gib-heads is shown in Fig. S7, where //. the height of the gib-head, = ij/. Cotter-locking Arrangements. — A simple method, and one that is used in nearly all cases, where possible, is to screw one or two set-screws through the rod until the point or points press against the cotter. To keep the burs, raised by the point of the screw, from interfering with the motion of the cotter, the set-screw bears on the bottom of a shallow (jroove cut on the side of the cotter, as shown in Fig. 89. The diameter of the set-screw need not exceed f '. The Irngth of the groove is equal to the travel of the cotter -|- the diameter of the set-screw. The travel of the cotter is the

â–

V.

^

J

Fill. V5- Frc. 96. Proportions of Rivet-heads. — The proportions given in the fijjurcs in terms of the diameter d arc those used by the CItampion Rivet Co. and agree closely with general practite. ''^Length of Rivet-shank. The length L (Fig. 92) for countersunk point-head ^^„.— and 2 plates ~^\d For countersunk point-head and 3 plates irf-f-J" For steeple point-head 1.2$^ For steeple point-head, large, machine-driven... 1.50^ For button point-head. ... \.z \d ^ The above proportions are good for ordinary boiler-plates, but, since the holes are -^' larger than the rivet, the shank

RIVETS AND RIVETED JOINTS. I3I ^o\jld be increased in length for thick plates to properly fill ^'^e additional annular space. The rivet-shank is usually about ^" smaller in diameter ^'^^n the hole and has a slight taper toward the point. Exercise 29. — Make a drawing of each style of riveting sHown in Figs, 92 to 96, making / equal to }" and selecting ^i^om Table 14, page 135, the diameter of rivet. For conventions see page 22. Scaie full size. Riveted Joints. — There are in common use at least five different styles of riveted joints, viz. : the single-riveted lapjoint (Fig. 97); the double-riveted lap-joint with staggered spacing (Fig. 98); the double-riveted lap-joint with chain spacing (Fig. 99); the single-riveted butt-joint with chain spacing (Fig. 100); the double-riveted butt-joint; the multiple-riveted lap-joint which has more than two rows of rivets in the lap; the multiple-riveted butt-joint which has more than two rows of rivets on each side of the line where the plates butt together (Fig. 103).

NOTATION. d = the diameter of the rivet-hole or of rivet when riveted up. p = the pitch of the rivets, i.e., the distance from the centre of one rivet to the centre of the next in the same row (Fig. 97). / _= the distance from the centre of rivet-hole to edge of plate (Fig. 97). r = the distance between the rows on double-riveted joints. r, = the distance between outside rows of rivets on lapjoints with welt-strip and butt-joints.

t:.

1 t

I32 DRAWING AND DESIGNING. m = the least distance between the etlge of rivet-hole ar»* edge of plate = margin (Figs, 97 to 103). t = the thickness of plate. /, = thickness of outside welt-strips for butt-joint. /, = thickness of inside welt-strips for butt-joint. t •=■thickness of inside weit-strips for lap-joint. f, ^ the tensile strength per square inch of the plate in lbs. f^ = the shearing strength per square inch of the rivet in. lbs. f^ = the shearing strength per square inch of the plate in lbs. fc = the compressive or crushing strength per square inch of the plate in lbs. R = the radius of boiler in inches on the outside of course of smallest diameter. A^ = the width of widest welt-strip. K = the width of narrowest welt-strip.

P = working pressure in lbs. per square inch. i>= outside diameter of botlcr-shell at course of smallest diameter. F = factor of safety. £ = efficiency of riveted joint. T = total tensile stress. a = area of rivet-hole = .7854^'. Strength of Single-riveted Joint. — There are five different ways in which a single-riveted lap-joint may give way: (i) Shearing the rivet, as shown at 1 in Fig. gi. (2) Tearing plate along the centre line of rivets, shown at 2, 2. (3) Tearing the plate through the margin, shown at 3.

RIVETS AND RIVETED JOINTS. 133 (4) Crushing the rivet or the plate in front of the rivet (5) Shearing the plate in front of the rivet (5, 5). The shearing strength of the rivet = — -X/,= ^X 38,000. ... (i) 4 The resistance of plate to tearing on centre line of rivet = {p-d)tXft (2> The resistance of the plate to tearing at 3 has been (ound by experiment to be great enough when the distance /is made equal to i^^, and, as this rule agrees with general practice, it will be maintained throughout this work. The compressive resistance of the plate at 4 is tXdXfc (3) The resistance to shearing the plate in front of the rivet as shown at 5, 5. = 2/ X / X /; (4> But if the joint is made strong enough to resist shearing the rivet or tearing the margin it will be strong enough to resist shearing or crushing the plate in front of the rivet, so that the latter may generally be disregarded.

The. thickness of the boiler-plate is PXRX F _ PR ^" ftXE "'w.ooqE • • • (S) The value for / should be taken as the nearest even sixteenths of an inch. Take E =■.70.

^

134 DRAWING AND DESIGNING. The thickness of dome-sheet may be calculated by the same formula. In locomotive-boilers the thickness of tube-sheets for f shells and over should be \" to -jV'« When shells are less than \" thick it is usual to make the thickness of tube-sheets equal to / -[- \" , The throat-sheet is usually made \'* thicker than the shell to allow for extra flanging. In thick shells, J" or over, ^" thicker will be sufficient. When the back tube-sheet is separated from the fire-box throat-sheet the latter should be made the same thickness as the fire-box side sheets, viz., -f^". The fire-box crown-sheet is usually made |" and the side and door sheets '^^" thick. Diameter d of Rivet-hole. — It is very desirable in designing riveted joints to obtain the highest efficiency and still maintain a proper tightness by using a pitch not too long for calking. In determining the diameter d of the rivet it is necessary that it should be strong enough to resist both shearing and crushing. Now the resistance to shearing is 4 while that of crushing is dtfc. which shows that the latter increases as the diametec and the former as the square of the diameter. So that if we can ob-

tain such a relation between the length of the pitch and the

RIVETS AND RIVETED JOINTS.

^33

diameter of the rivet-hole as will give the highest efficiency consistent with tightness the crushing strength of the rivet or the plate in front of the rivet need not be considered. To our knowledge the maximum limit for the length of pitch that will insure perfect tightness of the joint has never been ascertained by experiment or test, so that we have to depend largely on existing practice in determining the ratio between d and /. Mr. Wm, M. Barr in his ** Boilers and Furnaces" gives the following ratios between the thickness of the plate and the diameter of the rivet for single-riveted lap-joints, using the nearest even sixteenths of an inch, for steel plates and steel rivets (tensile strength of plates 55,000 lbs. and shearing strength of rivets 44,625 lbs. per square inch): TABLE 14.

%

Ratio of dtoi.

d

Decimal Equivalent.

Area of d. Sq. In.

Pitch of Rivets.

i

Decimal.

Working Fraction.

2.75 2.40 2.17 2.00' 1.87 1.78 1.70 Z.64 1.58

if" I ift"

.6875

.75 .8^25 .8.75 .9375 I.OOO 1.0625 1. 125 1. 1875

.371 .442 .518 .601 .6qo .7854 .887 .994 1. 108

1.892 1.897 1.934 1.990 2.058 2.133 2.205 2.298 2.386

2*^

A committee of the Railway Master Mechanics* Association on riveted joints in 1895 gave the following ratios between i/and /in their report for single-riveted lap-joints (steel plates

of 55,000 lbs. tensile strength and iron rivets of 38,000 lbs. shearing strength per square inch)

»36

DRAWING AND DESIGNING.

TABLE

15.

t

Ratios.

Mean Ratios.

d

>

E

?'■A" . «"

2.25 to 3.00 2.00 to 2.80

2.00 to 2.60 1. 71. to 2.42 1.75 to 2.35 1.77 to 2.33 1.60 to 2.10

2.62 2.40 2.30 2.06 2.05 2.05 1.85

it" 1*" 2"

58.6J( 5585 55.3; 52.8)J 50.2i»

Pitch p of Rivets. — The total strength of a boiler-plate is reduced by the rivet-holes, and the shorter the pitch the weaker the plate, but on the other hand if the pitch is too long the rivet will shear unless it is increased in diameter to correspond in shearing strength to the tensile strength of the net section of plate, but a long pitch and large rivet diameter are also limited by the fact that under high pressures such a joint is hard to make tight. The mean ratios between the thickness / of plate and the diameter d of the hole given in Table 1 5 are recommended as good modern practice. To find the pitch / in terms of the thickness of the plate / and the diameter d:

f

i^

Exercise 30. — Design a single-riveted lap-joint for a boiler 48" diameter and carrying a steam-pressure of 148 lbs. per square inch, plates to be soft steel of 55,000 lbs. teftsflc strength per square inch and iron rivets of a shearing strength = 38,000 lbs. per square inch. Scale 6" = i foot. (1) Find thickness / of plate by formula 5, page 132-

'; .

/

KIVETS AND RIVETED JOINTS.

137

(2) Determine diameter d bf rivet from the mean ratio able 15. (3) Calculate the pitch / by formula 6, page 1 36.

— 4 i

SedioaaiSS.

Fig. 97. ^Make complete drawings as shown in Fig. 97, giving actual dimensions in place of letters. Single- riveted lap-joints are commonly used for circumferential seams of steam-boilers. To determine whether a circumferential "Seam should be single- or double-riveted let us take the following example : Diameter of boiler 48". Steam-pressure per square inch 148 lbs. Diameter of rivet = .875". Pitch =r 2". Thickness of plate = .375''. The total force will be .7854jD'P= 1809.6 X 148 = 267,820.8 lbs. . (7) The resistance due to the rivets

_ .7854^'X «X/, ■" F

(8)

•.â– *â–

lid ZTJL*

JK = me mmxlser oc F = the facrnr of safiecr ^ 6. Taere fo re^ soEistxtiitzn^ wekxie

.6Qt X r^ X jS^Qoe . ^

and, sahtraftTBg t&e force from the resistaaoe» we have a c^^^ ference of 17.654.2 Ebsw m Exrar o£ the rivets. The total rrshtaiKTr of die pCite is

(/-^)X/X/f X « I-I25X.375X 55>OOOX 75

= 3SS.730 lbs., and, subtracting the total force. 267,820 lbs., from 288,750^ there remains a difference of 20,929 lbs. in favor of the platCt which shows that a single-riveted lap-joint is strong enough for the circumferential seams of a boiler of the above dimensions. Prof. Lanza referring to the efficienc>- of riveted joints in his ** Applied Mechanics" says: ** A riveted joint of maximum efficiency should fracture the plate along the line of rivets, for it is clear that if failure occurs in any other manner, as by shearing the rivets or tearing out the rivet-holes, there remains an excess of strength along the line of riveting, or, in other words, along the net section of plate — if in a single-riveted joint — which has not been made use of; but when fracture occurs along the net section an excess of strength in other directions is immaterial.

RIVETS AND RIVETED JOINTS. 139 **If the Strength per unit of metal of the net section is ^^^^>stant it would be a very simple matter to compute the ^**^ciency of any joint, as it would be merely the ratio of the '^^t to the gross areas of the plate. ** The tenacity of the net section, however, varies and this ^^-^ation extends over wide limits." This being so, the pitch in the last example is slightly ^^^nger than is necessary.

Double-riveted Lap-joints The arrangement of the '"ivets in Fig. 98 is called chain riveting and in Fig. 99 zigzag ^veting. The double-riveted joint is stronger than the single-riveted joint because of the greater net section oi plate and smaller diameter of rivet-holes. All longitudinal seams in steam-boilers should be at least double-riveted. Steel plates and iron rivets are considered the safer practice because of the danger of overheating the steel rivets. Wm. M. Barr in his ** Boilers and Furnaces" referring to the heating of steel rivets says: ** It is important that steel rivets be uniformly heated throughout, and not the points merely, as is the ordinary method of heating iron rivets; neither should they be heated as highly as iron rivets, and should never exceed a bright cherry-red. Particular attention should be given to the thickness of the fire. ** If excluded from free oxygen steel cannot be burned; if the temperature is high enough it can be melted ; but burning is impossible in a thick fire with moderate draft." Chain riveting with rivets of the same pitch has been found by experiment to be stronger than the zigzag riveting. See Barr*s " Boilers and Furnaces," page 85, where it states that the lap is wider for chain riveting, ''and no doubt the fric-

l^MAWIXfC M^n IK

ther woald be vitk the

fap €if tk dtttn livctii^.

Sectioa atSS. Fig. q3. Exercise 31. — Make the drawings for a double-riveted lapjoint, chain riveting, like Fig. 98, except that the actual dimensions should be given instead of the letters shown. Steel plates and iron rivets. Thickness of plate = \[\ p = 3-j^ ', d = li", / = iK r = 2^+ i", R = 30". Sca/e &' = ///. Calking need not be shown now.

Calculate the efficiency of this joint in comparison with the strength of the plate.

b'^.

RIVETS AND RIVETED JOINTS.

141

Taking/^ at 55,cxx) and/* at 38,cx)0 as before, the total strength of solid plate is /X / X// = 3-3125 X .625 X 55,000= 1 10,000 lbs. The strength of the net section of plate is (/-!/)//,= (3.3125- 1. 125). 625 X 55*000 = 75,735. The shearing strength of the rivets =- .7854^/'x 38,000 X 2 (for 2 rivets) =75,544, nearly equal to the strength of the net section of the plate. Therefore the efficiency of the joint is equal to 75.544

£ =

1 10,000

= 69 per cent nearly.

The following ratios of rf to / for double-riveted joints were calculated from the report of a committee on riveted joints to the Am. Ry. M. M. Association in 1895 :

TABLE la.

I" (-375) A" (-4375) i" OS) A" (.5625) tr (.6875) r (.75)

Ratios, Max. and Mm.

2.00 to 2.66 1. 71 to 2.42 1.75 to 2.375 1.77 to 2.22 j^.60 to 2.00 X.54 to 1.909 1.416 to 1.75

Ratioit, Mean.

1 d

/

a Area of Rivet.

K

2.33

i.

r

.6

71.4

2.06

^'*

.69

60.7

2.063 1*99

A"

3J"

.8866 •994

6y.O 68.4

1.80 1.72

3^" 3iii

•994 1. 107

6b 64.7

1.58

lA"

aJ"

I.107

62.7

To find \h^ pitch p for double-riveted lap-joints wfth steel plates and iron rivets. ^ 2y.aXf, . . 2X« X 38.000 , , , , f If, + ''=-73r??7o-5^ + ''- • ^'°> To find the distance between the centres of rows of rivets r (Fig. 99).

«.-. -

— •ESICX/IfG. zpArd Prof. Kennedy gives for the diagonal pitch, rwotf be found graphically or calculated by formula

. S(:r-r2d)Kfi+zd) 6

• . (II) Table 17 gives the distances(r) calculated by this formula (or the different sizes of rivets. Exercise 33. — Make drawings as per Fig. 99 of a doubleriveted lap-joint, zigzag riveting. / = f", ratio of t/to/a

1.80, A'= j;Find r b; Exercise 33 — sliovviii^ ihc iimc se^ini with a >:li^'1

â– von -j'j". itca/e 6" = i foot. 'iiid/ by formula 10. lir.uviii^'i similar to those in Fig. loo I ,1 Joiiblo /igzay- riveted longitudinaf :cd L-irciimferential scam for a steam-

boiler. / ^ i',.'. ./ calculated from the mean ratio in Table 16, / t-' be di'terminid from l.Tiiuila lo. /•' from Table 14, R = 29", r niav be calculated from formula II. Scale 6" = i foot.

Actu;

lilted from formula 11 to be jil.iced on drawing where letters

RIVETS AND RIVETED JOINTS. I43 sho-w in figure. Steel plates and iron rivets. Finish sheet

according to directions given on pages 19 and 20. L-ap-joints with Inside Welt-strip. — This style of riv»ting, shown in Fig. 101, is used for both single- and double-

t'/'i^-

riveting and possesses some of the features of the butt- ana lap-joint. In the single- riveted joint of this kind the middle row of rivets which rivet the three thicknesses of piate should be spaced according to the rule given for / in the singleriveted lap-joints on page 136 and the spacing of the outer rows = 2p. These joints are better than the simple iap-joint, but are XDore expensive, and are not any better than the butt-joint (Fig. 102), which is simpler and less expensive.

/

\.'

r^

.- .A » X

- .::rr t-:3. rratte ir-^i Fig. ^Ol) i- :::.; "Tie inrs'ie t-tt :f rlret::^ —

' — Jr.- ::.:o:. . . '1-4)

â– .t;

r. - r:: IT-T*

^? ;: 1 d .">uble-rivete(^ ::r.^. Fij. loi. Thff

'.vinj tabic:

5:ri vwiiTs.

.-

-

-

-

-

'_

1 • ^ â–

Etficicncy.

s

.

.

- j"

S70

;-_

--

- _.-

z

12* i • -. •»

?5-5

«

'.

-.

-,

•

i-'i*

^«i.3

» .•

# •

^

_T

• -

?s.o

1 /'

fi

â–

##

•

I*

"*

"I

^.

-i

15

j S4.3

The Double-riveted Butt-joint with Inside and Outside Welts. — Tliis 6ty\c of joint is a ven' common one for longi-

RIVETS AND RIVETED JOIXTS.

MS

t^uclinal seams of steam-boilers with plates f" thick and over. ^s shown by Fig. 102, the boiler-shell is rolled to a perfect *^Vlinder and the two edges of the plate which butt together

are held by two wclt-strips riveted to each other and to the ends of the plate. In a repeating section of the plate = 2p thero are two rivets in double shear and two half rivets in single shear. From experiments made by the English Admiralty and others it has been demonstrated that I rivet in double shear is equal to 2 rivets in single shear. For convenience wc uii! assuaie this to be so at present, although it is quite usual fur designers of steam-boilers to use a value of from 1.75 to 1.90

146 DRAWING AND DESIGNING. for rivets iii double shear; and, as the latter values agree more nearly with general practice for butt-joints, it will be necessary for us to modify our proportions in this regard, as will appear later. Therefore to prevent the plate a pullipg out from between the welt-strips the resistance to shearing will be

5 X a X/,, there being two rivets in double shear and two half rivets in single shear = 5 areas in single shcjir. Resistance to tearing the net section of plate at the outer row is {2p-d)tf,. Resistance to tearing the plate between the inner row of rivets and shearing rivets in outer row is {2P'-2d)t X//+ laf,. Resistance to crushing the plate in front of 3 rivets is ltd/, . fc may be taken at 80,000 lbs. per square inch for iron and 90,000 for steel rivets. Strength of whole plate equal in width to 2p is 2/ X tXft. Exercise 35. — Draw elevation and cross-section of a doubleriveted butt-joint with outer and inner welts similar to Fig. 102, given / = 3^", ^= 1.92/. If we consider the resistance to tearing equal to the resistance to shearing, then 2p = -^ 1- e/, .... (18) but this makes the pitch too long, because of the excess o( strength in the rivets against shearing. A better proportion

RIVETS AND RIVETED JOINTS.

H7

and one that conforms to good practice is .85(5«/.)

2/ =

//

+ d.

i^ and /, are, usually equal to /, but occasionally /, will be

ir^7

Fig. I02. found ^" thicker than /. The Hartford Steam-boiler Inspection & Insurance Company give all welt-strips -j^" less in thickness than /. For the remaining dimensions see the following table: TABLE 18. For double-riveted butt-joints with outer and inner welt-strips.

Ratio of

Diameter

Pitch.

/

dtot.

of Hole.

I

r| = a/

K

N

Average.

J

•ft

2.19

W

af."

^ff'„

A"

<

9r

JL"

1.93

r

2 I"

»iV

5J"

loi"

JL"

1.92 1.92

,r

2*

2\" 3"

5f

1 1" 12"

r

1.72

â– *'

«r

lA" .

3i"

ej"

I2f'

V

148 DRAWING AND DESIGNING. Triple-riveted Butt-joint with Outer and inner Weltstrips (Fig. 103). — This joint has three rows of rivets on each side of the butt. One row passes through the boiler-plate and one welt-strip and two rows pass through the sheet an4 two welts. The resistance to tearing along line xx is

Fiii. 103The resistance to pulling the plate out from between the welt-strips is 9X « X/, X .85.

\'*'

Vyi

RIVETS AND RIVETED JOINTS. 149 The resistance to tearing on line yy and shearing rivets an XX is {2p-2d)tf,-\- \af.. A glance at the figure will show that this joint cannot fail ilong the line ss, because there are two rivets in double shear undone rivet in single shear in addition to the net section of plate, which is equal to the net section on yy. Exercise 36. — Make the drawings for a triple-riveted buttjoint like Fig. 103. Steel plates and iron rivets, t = ^", rf s= li", ScaJ^ 4" = J foot. The other dimensions may be takyi from the following table : TABLE 19.

'

i

f

.

'

'

"

Efficiency.

In.

Id.

In.

In.

In.

In.

In.

Per Ccnl.

.!

H

»«

}|

â– 1

si

t3

86,1

I

3A 3

J

â– j

fl|

â– 4

B6

11

It

l|

91

15

S()

3

»A

â– 6

S6

i>

t

3A

't'

n

'4

86

H

3

i;



r..i. , .J. L..e DilC*vwT a? shown

- â– V- mm ^

f\

» .

t1..I '■^ l-'lt.b>x- V..— •••^•. .•

■•■■- l- •â–

^ -.•■.: •. r. :i > : r. e l ri-^zcn- tui r 1 ... i^^i^r. :.- 5:1: tabic for an .-: ..:r.-- T'-Ssuro I So lbs per -. . .\\ :.-.e Empire State Ex. : ...I'.A.-.r.an. Supt. of Motive .-:.-: -':: 'W> a cross-section .vr. -bar which consists of two

\

4'ETS AND RIVETED JOINTS

IS'

^ //PO" LM£0-

^wrought-iron plates 5" deep X J" thick and welded together |«t the ends. The fire-box crown-sheet is supported by J" ivets, which, passing through a washer b and between the

plates A of the bar and through thimble G, is riveted on the underside of the crown-sheet as shown. These rivets are placed from 4" to 4i" apart, and as many as the crown-bars will accommodate at these centres, the end bolts being placed about 4" from the inside of the fire-box side sheets. As seen from the figure, the crown-bars are placed in a transverse position

/y

DKAWISG A\D DESIGNIXG.

on the crown-she^, and as many as the longitudinal length of the sheet will allow, with equal spacing, about 4V apart. Should these bars be insufficient to support the crown-sheet against the downward pre^ure of the steam, which is equal to the area o\ the crown-sheet X the stcam-pressure per square inch, then what remains is held up by s/in^-stays hung from the outer shell and fastened to the crown-bars by links and pins, one link of which is shown at J in the transverse cross-section. The flat upper part of the back-head, which has no staybolts passing through it like those which bind the fire-box and outer shell together, as shown at />, is stiflcned with a Uncr I" thick, the shape of whicli is shown by dotted lines on the transverse section, and to this liner arc riveted as many lengths of 3" X 3" angle-iron as can be placed on the liner, with a clearance-space of only about f " between. To these angleirons are bolted longitudinal stay-rods i^" in diameter similar to that shown in Fig. 106, To support that curved part of the outside shell just above the fire-box transverse stay-rods C are carried between each crown-bar, screwed through the shell on each side, and riveted over on the outside. The body of the rod is i^" in diameter and the screwed ends ij" diameter. The fire-box stay-boits Z> are screwed through both firebox and outer shell and riveted over outside and inside. It will be seen that while the screwed part of the bolt isj" diameter the body is turned down to J", which reduces its stiffness and allows it to give somewhat to the unequal expansion of

the fire-box and outer shell of the boiler. In certain places the stay-bolts are more liable to break than in others; in such

RIVETS AND KIVETED JOINTS. 153 places hollow stay-bolts are used, so that when broken they may be easily and quickly detected.

Hollow stay-bolts have an \" hole drilled completely through from (ircrbox to the outside of the outer shell, so that

>?

= . - ~^=^SJ.\J.VC.

r.^ Ttii.n ind water will 5

oon

'.: r _ _-.. -Mr "himbles is shovn "T"'- -- --* ci^ntre line 6' 6" .- - V. z . i-^.rjdir.al centreline ■" -'-"• •—c tr-insverse and

: â– ^:rl:ct the

:..-.: ts should

r: ; tn:s is a

: ."

8J

6i

m

lOl

iS

ei

6(

«3

>Ii

S

34

11

S

t

1 41 161

:n

9

a6 as

"4 26

tmlts to be determined from equation (18), and the diameter of the bolts from equation (19) The remaining proportions to be worked out according to the student's judgment. ^ The Sellers Clamp Coupling (Fig. 120). — This is a ^,^^ie^ form of a muff coupling which is turned to a cyltn*

DRAWING AXD DESICMJXG. l-^lrical form on the outside, but has a double conical s I inside. Two conical sleeves or bushes turned to 6t

Iniilde of the muff and bored out to fit the shafts ftre puUedl together by three bolts. The sleeves are split on one side I through one of the bolt-holcs, so that the more the bolts are ] icrewed up, the tighter the sleeves clamp the shafts and bind i them firmly loKethcr. Keys arc also used to further prevent I Bhpping Exerciie 47. — Make the drawings shown in Fig. 121 of a | Sellers clamp coupling. Scale full sise. The taper of the conical sleeve is 2%" per foot of length ] OH tht diamrlrr ; e.g., if the sleeve was 6" long and the large 1 diameter meaitured 4", the small diameter would measure 2J' For the dimensions of the Sellers clamp coupling for J various diameterii of shaft, use the following table.

fe

SHAFTING AND SHAFT-COUPLINGS. 173

DRAWING AND DESIGNING,

SKLI-KKS

LAMP

-OOPLINCS.

D

*

-

^

J

D

J

c

£

^

li"

*\"

Sf"

at"

1*

â– h"

3"

8i"

..I"

4"

6"

r

t\

bt

3|

4

It

-)!

"*

4

bl

I4J

3

3i

bk

8t

If

S

â– !

i2f

i«*

71

TO

It

at

Tf

qt

If

6

aii

11

tf

2i

7»

loi

41

122 shows three views of 5 somewhat like the Sellers r bolls nor keys, the conical lund nuts threaded into the at the side, and when they )lit sides arc at right angles allows a key-driver to be jenings (after the nuts have ler bush when it is desired

Frictional Cou"''"*' — ^'t^ Butler's frictional ci coupling, except that i bushes being held in o muff. The conica! are in position on su to each other; this ai jenr introduced through one of these been removed) to drive out the to remove the coupling from the shaft. The bushes are guided into position by small dowel-pins which enter short

grooves provided for them inside the muff. The J" round holes shown in top and bottom at the centre of the muff are used to see when the ends of the shafts come together, for then only will the coupling be in its proper position. Exercise 48. — Make complete working drawings of the Butler coupling like Fig. 122, except that the shaft shall be of steel and the' sectioning shall be appropriately colored instead of hatch-lined. Scale = full size. The threads on the lock-nuts should be that number pe inch used on a pipe whose outside diameter is nearest to tht.

SHAFTING AND SHAFT-COUPLINGS, l?S

I/G

DRAWING AND DEStGNlNG.

outside diameter of the nut. The lock-nuts are screwed into position by means of a spanner wrench having projecting pieces which fit into the recesses shown in end elevation. The taper of the conical bushes may be made }" in 12" on the diameter. The faces marlced with small f are to be finished. The principal proportions of this coupling are as follows: d = diameter of shaft ; D = diameter of muff = 2.2$d; L = length of muff = 4d. Stuart's Clamp Coupling. — This coupling, shown in Fig. 123, differs from the Sellers coupling in having tapered

Fig. «3. wedges instead of conical sleeves; these tapered wedges and opposite halves of each end of the muff are bored to the size of the shaft. Studs and nuts hold tlic wedges in place, making, on the whole, a cheap and effective coupling without the use of keys. Exercise 49 — Make drawings of a Stuart's coupling as

shown in Fig. 134 for a ij" shaft. Scii/e = full sise.

SHAFTtNG AND SHAFT-COUPLINGS, \J7

T^

— —

\

r

"J*

^- \

! 1

r

J)

i^

sT^. ^

. 1( .

vo

^

lai a iflit of tbe Sangc coup ecdcnul diameter of Ibe ', and take an t for tfe pmfMKtions. ScaU Let /?. asd D. be tie isTcntt] and the externa! diameter, respectively, o: the b^l^ow shaft; then tram equation (15) we have

" = \ -IT= dianieter o: an eqjh-alent solid shaft = unit. J — diameter of bolt: n = number of bolts = .25/? + 2; R = radius of bolt circle = ^ + ^ ^S*^ 2 Resistance to shearing of bolts = resistance to torsion of shaft divided by R.

t^r (U-^*^' ^'"^^ ^'A

SHAFTING AND SHAFT-COUPLINGS, 1/9

•-*

KW 31

-^ ^

--

-

^

X

-

-

d

^

,

-

-.

«

s'

S

sH

t

»t

>^

3«

a

s«

*

i

sA

=

â– i

%

*â–

at

J»

1*

»

n

=*

^

'v

rr

=«

i+

i

4

e

ii.

•

^

r=

s

This formula gives a thickness somewhat less than is used iu practice. Z89

190 DKAU'IXC ASD DESIGNING, D. A. Low gives

+'.

and the values of k and c as follows:

TABLE 24.

Casl-iroD steam or water pipes .. Ca*l-iroit steam -cylinders Lap-welded wroughl-iron lube Solid dmwD steel lubes Copper steam-pipes Lead pipes

For foundry reasons < _Ei££IJ^ifl!lld.never be les^^ thanj^" thick, and loag.iengLu .ot less than ^". For tables giving the thickness of pipes for various pressures and equivalent heads see Kent's " Mechanical Engineers' Pocket-book," p. 189.

PIPE-COUPLINGS. Cast-iron Pipe-coupltngs — The most common method of connecting cast-iron pipes is by flanges cast on the pipes as shown in Fig. 131. Exercise 55. — Make drawings of a cast-iron pipe>coupling like Fig. [31. £>=?>". Calculate remaining dimensions by the following formula. Scale 6" = i foot. t = 0,023/) -t- 0-327; /^=0.O33P-|-o.56;

PIPES AND PIPE-COUPUNGS. 19* E= i.i25/? + 4-25; C— 1.0927?+ 2.566; d = o.owD ■\- Q.-jy, «= number of bolts = 0,78/?+ 2.56;

to = weight of pipe per foot = 0.24/?" + %D; W= " " flange = .oolZ'* + o.l/?' + i? + 2. This joint has the flanges faced all over, and is used for essures up to 75 lbs. per square inch (170 ft. of head); for

Fig. 131.

^KT pressoFes the joint may be made with a string smeared tfa red lead between the flanges or a lead, india-rubber, or ■tt*-percka ring. XutcIm 56. — Hake drawings of a cast-iron- pipe flange Dpling. Fig. 132. Inside diameter of pipe to be 9", other WMiinni tn hr tnlrrn from Table 25. Scale 6" = 1 foot.

DRAWIXG AND DESIGHINQ.

TABLE 2a. ETANDARU CAST-imON I

StrcNOB

D

'

"

'^

^

£

d

Tbre°>d *t

/

401)

â– tt

5/8

6

./8

8lS

«/4

al

7

1050

1/4

1/4

s/s

1/4

4>

It

4Wj

.3/ .6

»t

s/a

S/lb

7

9

•i/16

800

4i

WB

7

V4

S/16

-i25

.S/it

3/4

1630

1/8

.^61

9

1/4

a36o

.«o

â– -V

V4

V8

.^3q

>l

ni

V4

4190

VB

1=80

U

15

16-0

V8

H\

•A

.(.

VB

"

â– 79

"

.4

li

â– 9

3/8

1470

% adopted by a and [he Master Steam anj llol Wate; Fit Slzea up 10 14" diameter arc designed for ^^

: of the A.S.H.E. â– rs Association In July, 1B94, > lbs. preHura per iqakre fai^

PIPES AND PIPE.COUPLINGS. m Ipes— that~P rater or gas. Fig. 143 shows a joint of this kind. About alf of the space between the spigot and socket is first filled 'ith rope gasket and into the remaining half is poured molten ;ad, which when it cools is calked tightly into the socket 'ith a hammer and round-nosed tool.

Exerdse 56-4. — Make drawings of a spigot-and-socket coupng for an 8" cast-iron pipe carrying a pressure of lOO lbs. er square inch (Fig. 133). Scale 6" = i foot. Same elevations and sections as in Ex. 55. Calculate the imensions from the following proportions : • 0-^ tnternal diameter of pipe;

« Aickness of pipe =

- -|- f from equation (2) ;

f, = t + .21; ', = '. + *■■; '. = '. + f': A = .07iD+2r: fi = .iZ)+2r; C=.o6D-^ i": f = 1»," to t"; ' + •7

E^nrcise 57 — Make ' socket cast-iron pipc-co di«nictcf o( pipe 10".

Ex. 55. S(«lt6"— I /iwt.

liawings for the spigot-andlown in Fig. 134. Inlenial wj and seclioKs similar V>

B -T

The dimensions for this problem are to be calculated from the proportions given for Ex, 56. The turned and fitted part E is made with a taper of f " in 12". Exercise 58. — Make working drawings of an 8" cast-ironpipe flange coupling like Fig. 135. Elevations vaA sections as in Ex. 55. SkiU 6'' = / foot. Dimensions to be taken from Table 25.

PIPES AND PIPE-COUPLINGS. I9S These pipe-ends and flanges are strengthened with ribs drawn at an angle of 45° with the axis of the pipe, and the

Fig. I3S. joint is made by means of fitting-strips cast on the flanges equal in width to the thickness of the pipe. The faces of these strips are finished perfectly square with the axes of the pipes, and before bolting up are smeared with red lead. Exercise 59. — Make drawings of the loose flange coupling for a copper pipe shown in Fig. 136. Inside diameter of pipe 8". Scale 6" — i foot. This joint is the invention of Mr. R. B. Pope of Dumbar-

Kt«^«

aafcaf «a«aBM. omi^b^ ■■■» mva^dcd, i: Ar faHcr « fBAaed. fc ii cndm fimi

1!!!

i'. ti * J >'■• : !!•?? ■A '-i : I

7 • In ift

?!

ii';!

it t^ >^

Wrought-iron and Stee! Pipe-coaplings. — Fig. 13; rhowa a verj' cmcien: form of joint for wrought-iron pipes. The Har-oCci cr.'Ji of the pipes arc countersunk into the cast flan'-e rin^s, and the bolt-heads are also countersunk about f of an incli. I'.etween the flanged ends of the pipes is placed a ring of lead }" thick and from f" to f" wide. Exercise 60. — Make drawings of the joint shown in Fig. 137 for a 6 ' wrought-iron pipe. Scale full sise. A should be made equal to i.z^d. t may be taken from

Table 7. Remaining dimensions may be taken from Table 26.

PIPES AND PIPE-COUPLINGS.

The "Converse " joint for wrought-iron and steel pipes is shown at Fig. 138. It is manufactured by the National Tube Works, McKeesport, Pa. This joint consists of a cast-iron sleeve with a space for lead at each end; there are also interna] recesses plainly shown in Fig. 138. into which are

Fic. 138.

inserted rivet-heads on the ends of the pipes, and by a turn of the iHpes the flanges become locked in position. Molten lead U poured into these recesses around the rivet-heads and ti^tly calked at the ends of the sleeves, as shown in Fig. 139.

198 DgAlVTfrC AND DESIGNING. Exercise 6t. — Make drawings of the Converse joint fori 7" wrought-iron pipe, according to the dimensions given in Fig. 139- Elevations and cross-sections same as in Ex. 55. Scale 6" = / foot.

Fig. 139.

Screwed - flange Pipe - coupling. — Fig. 140 shows a wrought-iron pipe-joint made by screwing cast-iron flanges on the ends of the pipes and held together by bolts. It is used by the Philadelphia & Reading Coal and Iron Co. for their steam-pipes. The threads of the screws on the pipes are made according to the Briggs standard. The lugs shown in the figure on the right-hand flange are cast on, and have their inner surfaces finished to fit the cylindrical fitting-piece on the other flange. The ring shown between the flanges ia of gvm rubber and makes the joint steam-tight. The pipes

are made in lengths of from 16 to 20 ft. Exercise 62 — Draw a screwed-flange pipe-coupling like Fig. 140 for an 8" wrought-iron pipe. Scale 6" = t foot. Dimensions may be taken from the following table :

PIPES AND PIPE-COUPLINGS.

60— - •

. V-

"W

â– ^

=«

>•

: T/ll -1

V4

-s^

~i

sc

1/.

*

ft

»

V*

3*

«

&•

J-

*

a*

^

: : : c-

C — f -^ i4i si«ws a screwednBlc-«i» pipe- Toe socket is : ta£ «f coupling made with angle-iron for a steel pipe. The angle-iron is rolled and welded into rings and riveted to the pipes. These flanges are used for either wrought-iron or

; of a

Fig. 143. steel pipes. The joint is made steam-tight by r lead ring inserted between the flanges as shown. ExerdM 6$. — 'Make drawings of a steel pipe with wrought iron flange coupling like Fig. 143. Nominal size of pipe 8" diameter. EUvatiens and sections like' Ex. 5;. Scale 6" = i foot. Couplings for Brass and Copper Pipes. — The coupling shown in Fig. 144 is used *on locomotive-boiler feed-pipes, injector-pipes, etc. The sleeves {a) and {H) are brazed to the pipes, and a thin copper gasket placed between the ends of the sleeves makes the joint thoroughly tight when screwed up with the fluted nut (c). Ezerdie 66. — Make drawings, as shown in Fig. 144, of a brass pipe-coupling, outside diameter to be 2i". Scale full size. The dimensions may be taken from Table 28.

' ..

. . . . i. y «- ^ i

jr

â–

Pi

i r/. 3/. '1 i\ 7/a, >i ' 31

3/8 s/e 3/> 5/8 7/16., 3/4 T/tfJ 3/4 7/l6| V4

t

1

PIPES AND PIPE'COUPLINGS.

Form OF Section

AREA OrStinoN

Modulus OF Section 1

bfo-d)

12 , .118b

1 D-J » D

r , *«£« Modulus OF FOBN Of Section, J 5jj„„sj„,5,z^

I BD-bd » D

1 bD'*B pjral'ei to the axis of the shaft and the 5:-.a:: :;'r-r--A:;^ i: :"r,e bciring surface. Fig. 164, the bear-

JTiC :^ •"' -.':\.~:-I>;.i"-^. \Vhe:i :h:s t\-p-Iindrical, conical, or spherical, of which the cylindrical is the most common form.

BEARINGS, SOLE-PLATES, AND WALL BOX-FRAMES. 20/ To limit the longitudinal motion of journals the shafts are ♦umed down or have collars forged upon them to form shoulders which come in contact with the faces of the bcariniKS upon which the journals revolve. When practicable the length of journals should be about one per cent greater than that of their bearings. The Area of a Bearing is the width of the chord of the arc in contact with the journal, multiplied by the length of the bearing. This is sometimes called the projected area, because it is the area of the contact surface projected on to a plane perpendicular to the direction of the pressure. Thus the area of a cylindrical journal-bearing, Fig. 164, is D X L. The area of a pivot- bearing, Fig. 278, is I nD" ~'i ■T)^ ' . The area of a collar-bearing is ~ {D" — B*)N. Where -^ U is the diameter of the shaft Z>, is the outside diameter of collars and N the number of collars. 4.1I .^ • ^^ Solid Journal-bearings. — The simplest form of journalbearing is made by drilling a hole through the frame of the machine, and to provide sufficient bearing surface the length of the bearing is increased by casting projections, which are termed bosses, upon the frame, as in Fig. 145. In this form of bearing there is no provision for wear, and the shaft can be returned to its initial position only by renewing that part of the frame that carries the shaft, or, when the hole wears oval, reboring the bearing sufficiently to fit it with a cylindrical sleeve or bush, as in Fig. 146. Such a bearing may be provided with a bush or lined with soft metal, and can be restored to its original condition by renewing the bush or lining. The end movement of the shaft may be limited

208 DRAWING AND DESIGNING. by making the diameter of one of the journals less than the diameter of the shaft, thereby forming a shoulder which limits the end movement in one direction, and securing a separate collar to the shaft, by means of a set-screw or taper-pin, in such a position as to limit the end movement in the other direction, as shown in Fig. 145. Another method is to make the shaft of uniform section throughout its length, limiting its end motion by means of two separate collars which may be arranged in three difTcrent positions. Exercise 67. — Draw two i{ I solid journal-bcanngs supporting a shaft 2" in diameter, making the area of the bearing surface 6 square inches, and show an arrangement for limiting the end movement in cither direction by means of one loose collar, as shown in Fig. 145. Draw also one bearing ij" in diameter with a brass bush or sleeve, as shown in Fig. 146. Make / equal to o.i(/-|- ^". Parts dimensioned in decimal

BEARINGS, SOLE-PLATES, AND WALL BOX-FRAMES. 209 fractions are proportional to d. Complete and fill in the actual dimensions to the nearest sixteenth. Scale full size. As the shafts supported by solid journal-bearings cast with the machine- frame have to pass through one bearing to the other, this form of bearing cannot be used when there are projections on the shaft. A solid bearing can be used, however, for supporting a shaft upon which there are projections, by making the bearings independent parts and securing them to the machine-frame by means of bolts. By this arrange-

ment the shaft is turned down on the ends to form the journals, and one of the bearings is placed on its journal before it is secured to the frame. This form of bearing, Fig. 147, consists of a hollow cylinder cast upon a base through which bolts are passed into the machine-frame or si^pporting bracket. Fig. 147 shows a design of a solid journal-bearing used for supporting the valve-gear reversing-shaft of a locomotive. Such a bearing can be used for this purpose because it is subjected to a comparatively light load, while the journal has a slow and intermittent movement. The length and shape of the bearing in this design are determined by local conditions, the bearing being carried forward further on one side of the base than on the other to suit the shaft. The width of the base is determined by the thickness of the frame, and is provided with strips on the under side to facilitate fitting. Exercise 68* — Draw an elevation and plan of a solid journal-bearing of the form shown in Fig. 147, making d = 2\" and L = 2d, The parts dimensioned in decimal fractions* are proportional to d. Scale full size. ,

2IO

DRAWING AND DESIGNING.

Construction. — First draw the centre lines and cooiplete the cylindrical part of the bearing. Make the distance a equal to the outside radius o( the cyh'ndrical part -f-f,{tbe

^y

A

I

Fig. 147. radius of the fillet, which we will make equal to. say \") + half the distinct; across the angles of the nut + J" for clearance. The distance b can be made equal to half the distance across the angles of the nut + i '■Dt7ided Bearings — Where the conditions are such that the shaft cannot be placed upon its bearings endwise, the bearings are parted and the parts fastened together by means of bolts or screws. The division is generally made on the line normal to the resultant pressures on the bearing.

BEARINGS. SOLE-PLATES. AND WALL BOX-FRAMES. 211 In Fig. 148 is shown what is generally termed a two-part bearing. It consists of the block P, upon which the journal is supported, and the cap C, which is secured to the block by the bolts CB. In this design the journal is intended to be lubricated with semi-liquid grease which is passed through the opening O. The bearing is lined with Babbitt metal, .cSZ) + tV' thick. The holes through which the holdingdown bolts pass are made oblong to horizontally adjust the pedestal. Wall Box-frames are built into the wall for the purpose of supporting a bearing for shafting which passes from one room or building to another. Fig. 149 shows a wall boxframe with an arched top to support the wall above it. On

die sides are cast projecting webs W which fit into the wall to Inep the frame from moving endwise. The upper side of the base Is provided with raised machined strips ^5 upon which the pedestal rests, as shown in Fig. 1 50, and at each end of this sniface are projections S, on the sides of the frame, which â– K also machined. To adjust the pedestal horizontally, wooden keys of the necessary thickness arc fitted between the sarfape S and the pedestal base. The height H is equal

to the highest point oi the pedestal cap when raised clear of the cap-boits CB -^ about 6" to allow the engineer to remove the cap. The length I, is equal to /. the length of the base, -f the amount of horiionCal adjustXDcnt allowed on the pedestal

-j- V'* "^^ width :t- is made . uit the thickness of the wall, which is usually built to average from 8" to 12". The proportioning of such a' piece is largely a matter of experience, none of the parts being calculated for strength. Exercise 69. — Draw a pedestal and wall box-frame of the designs shown in Figs, 148 and 150, placing the pedestal in position on the wall box-frame, to which it is secured by two square-headed bolts the heads of which project below the base. Make the pedestal to suit a shaft 2^" in diameter, the length L equal to iD, and the width w of the frame equal to 8". Show a half-elevation and balf-sectional elevation of the pedestal, and an elevation of the wall box-frame, also a plan view of the pedestal with half of the cap removed, and in combination with this view show a section of the wall boxframe at the line WS. Make also an end view of the pedestal

BEARINGS, SOLE'PLATES, AND WALL BOX-FRAMES, 215 aiid a sectional end view of the wall box-frame. All parts of the pedestal are proportional to the diameter D of the journal. Fill in all dimensions omitted. Scale full size. Construction, — Draw the vertical and horizontal centre lines of the journal, then determine the distances from centre to centre of the bolts by drawing the line i which represents the top of the cap-flange, and the arc 2, which represents the top of the cap at the centre of the bearing. The centres of the cap-bolts can now be determined by making the corners of the nuts from -^" to \" clear of the fillet which joins the lines I and 2. It is obvious that the bolts may be brought nearer together by either increasing the thickness of the capflange or cutting out the curve 2 around the nut, but on small pedestals for line shafting this is unnecessary. The radius r is made equal to half the distance across the angles of the nut + i" for finish. The distance from centre to centre of the holding-down bolts is equal to the distance b -}- the horizontal adjustment (equal to the length of the hole — diameter of bolt) + the diameter of the washer -}- the radii of the fillets, which may be made equal to about J". Determine the radius r of the arched top of the wall box-frame by making

e F, the versed sine of the arc, equal to — . Half the elevation is sectioned, to show more clearly the method employed to keep the Babbitt lining from turning with the shaft, the form of head on the cap- bolts, and also that the diameter of the holes through which the cap-bolts pass is greater than the bolt diameter. The plan view is shown with the cover removed from one side of the bearing, to show the form of that part of the bearing through which

214

DRAWING AND DESIGNING.

the shaft passes. The fitting-strips on the under side oJ th* base are of the same proportions as in the previous exercise. Wlien practicable it is usual to provide the piece to whicrli the bearing is fastened with fitting-strips also, as in Fig. ijelP' Post Bearings. — When the bearing has to be secured C:=^o I vertical surface, the base is cast on the side, as shown f n Fig. 151. In the design shown in Fig. 152 it is necessarj' cn^o provide the cap with four bolts because of the webs W, whic^ ^ 'are in the way cf the bolts '~-= — placed on the centre ^^= in Fig. 14S. The bearing jed in this case for tw '■grease-cups, which are screw o the cap at the tappe-— ^

holes O. The cap-bolts are I are being screwed down by side of the box. Exercise 70. — Draw the el section, as shown in Fig. 152, top pro]

m turning when the nut" ions // cast on the unde-

and an end view half ir"=3

V also a plan view of the^^ :ed from the elevationMake D = 2j", and L = three time^ /?. Parts not dimensioned are im the same proportion to D as in the preceding exercise. Sca/e half sise. Construction. — Draw the centre lines of the bearing, taking care to leave sufficient space to draw the plan. Mark off the distance that the bearing projects from the post, then determine the length and width Fig. 151. of the base. The centres of the bolts PB should be in a distance at least equal to the radius of the washer -|- \" from the ends of the base.

SEARINGS. SOLE-PLATES, AND WALL BOX-FRAMES. 21$ Fig. 148-

2l6

DKA WIKG

The vertical adjustment a is made equal to ij". As the oblong holes are cored, the width € is \" greater than the diameter of the bolts. Wall Brackets are employed to carry pedestals which support a horizontal shaft running parallel and near to a wall. The bracket, Fig. 153, is fastened to the wall by means of three bolts which pass through it and the wall. The pedestal

is secured to the upper surface by square- or T-headed bolts which slide in the J-shaped slotS which runs the whole length of the bracket. By this arrangement the distance that the pedestal is from the wall can be adjusted. Exercise 71. — Draw a wall bracket to the proportions given

in FiuglH uea gr together by screwing down the cap C^ bvmeans of the bolt s C B- I'o keep the cap from being screwed down too far, causing the bushes to bind the journal, the space between the cap and the pedestal is sometimes filled with hard wood and the wear is taken up by filing down the hard-wood distance-

BEARINGS, SOLE-PLATES, AND WALL BOX-FRAMES- 231 pieces, thus allowing the cap to be screwed down a limited distance. Others make the bushes in contact with e ach other, as in Fi^ T, j^, when the^ushci fit the sliaft, and when they become worn -they-axe filed down sufficient!}; to compensate fpr ^h^ 'Ytari ^^"â– n thf hiishfic An nnt t;nmf in contaCt With each other and no distance-pie ce is used, the cap-bolts should be provided with double nuts. After the pedestal has been'

Fig. 169. adjusted to suit the shaft, it is held in position by the bolts P B. The holes in the base- and sole-plate through which the bolts P B pass are made oblong to allow the pedestal to be moved along the shaft or transversely to it. To farilitatp thy fiftJu g of the pedestal to the piece up on which j» if* ramVH (h/- hase.is. jUDvIdfd With fitting-strips around the edges and across the centre. The oiUcup is usually

232 DRAWING AND DESIGNING. cast with the cap C, or screwed into the tapped hole 0, Fig. 169. On pedestals having journals less than 3" in diameter O may be made to receive an oil-cup with a \" pipe ti^ shank, and when over 3", with a |" pipe tap-shank. Exercise 76. — Draw a general arrangement of a pedestal and sole-plate, Fig. 169, substituting the form of bearing shown in Fig, 164, Show a HALF elevation and HALF SECTIONAL ELEV*Tir»M t-h.. nlanc of section passing through the centre of the TALF PLAN and HALF SECTIONAL PLAN, the passing transversely through the centre of the ; 1 he elevation project a HALF END-ELEVATION i H. ONAL END- ELEVATION", the plane of section passi the centre of the pedestal. Make the length of the h« gh the sole-plate and pedestal-base sufficient to all< iestal to move 1" in cither

direction. Make D = 4' d..u „ = 2D. Scale half sisr. Construction. — All parts dimensioned in decimals are in terms of D {the diameter of the journal). Parts marked in inches are constant. Any parts not dimensioned can be determined by the student from knowledge derived from previous exercises. A method of drawing the joggles/ is shown at Fig. 169, which will be readily understood from the drawing. SELF: LUBRICATING- PEDESTAL,,^ In this design, Fig. 170, an oil reservoir OR is formed on the under side of the bearing, in which loose rings R are revolved by their friction on the journal, thereby raising a continuous supply of oil to the upper side of the bearing, thus keeping the journal thoroughly lubricated and not

BEAJUNGS, SOLE-PLATES, AND WALL BOX-fKAMLS. 233

234

DHAliJ.ya AND DESlCNiNG,

wasteful, as the surplus oil that flows out of the bearing is caught in the chambers CC and carried back to the reservoir OR. As the same oil, in this form of lubricator, is being used repeatedly, after a time it becomes dirty and thick and is then useless. Dy removing the screws S the old oil is drained of?, and the reservoir can then be replenished by pouring new oil

into the openings in the covi large, so that the e This pedestal is a will be very little we; cap C. The lower the sketch. Fig. 171. vided with projecting f,

which fit upon corresponai and are made concentric witfi bush it is iicjt necessary to w,

:r. These openings arc made t if the rings arc revolving. r/oT^iS. The thermal units per minute Pi's , , P^iSW , , . , ^ P»S . , , = -^-g . and A = y^, from which L - ^^g^, in mches.

With steel journals running in bronze or white-metal bearings, having continuous lubrication, /(, the coefificient of friction may be taken at .OO56. Exercise 77. — Design a self-lubricating pedestal for a shaft 6" in diameter, of the form shown in Fig, 170, to carry a load of 35,000 pounds, and run at a speed of 300 revolutions per minute. Show a HALF KLEVATION, HALF-SF.CTIONAL ELEVATION, the plane of section passing through the centre of one of the lubricators, a HALF END klevation and HALF TRANSVERSE SECTION', the plane of section passing through the pedestal at thecentre, a HALF PLAN of the left-hand side of the pedestal, a QUARTER PLAN With the cover (C) removed, a QUAR-

BEARINGS, SOLE-PLATES, AND WALL BOX-FRAMES, 237 ER-SECTIONAL PLAN, the plane of section passing through le centre of the shaft. Scale 3'' to the foot. Make also full-size drawings of the lower bush, showing a [ALF ELEVATION and HALF-SECTIONAL ELEVATION, a HALF ND VIEW, and a half transverse section, and a plan nd elevation of the ring-joint as shown. All points are proportional to the diameter {D) of the ournal, except those parts which are constant for journals A various sizes.

M^^ ^

11 ^

H> U

*!♦

â– ^

/

U } } t^

i

i

CHAPTER VII.

BELT GEARING.

Belts. — Amc for belting are Canvas, camel-hair, bands, flat chains. The most common Cotton, the latter oft known as gum belts. Leather is more dur.

'"■crent kinds of material used gutta-percha, India-rubbet, wire or hemp rope, steel i\ practice are leather and ated with India-rubber and ! gum under most conditions, 'I but for main driving the lattei is auperior, having an adhesion which is claimed to be one thjrd greater than the former. Transmission of Motion by Belts. — Motion may be transmitted from one pulley to another with uniform linear velocity by means of a belt, provided there is no slipping of the belt on the pulley; i.e., regarding the belt as inextensible every part of it will have the same velocity as the outside rim of the pulley. Referring to Fig, 171, let d, and d, be the diameter of the driver and driven pulleys respectively, and let JV, and N, he their revolutions per minute and F the velocity of the belt. The speed of the rim of the driver

r N, :

(0

BELT GEARING.

339

Fig. 171. speed of the rim of the driven

= d^n N^= V .

' (a)

N, = d,«N, or d,Ar, = d,N, or ^| = ^. (3) 11 questions concerning the velocity ratio of belting ^y diameters should be taken to the centre of the belt

J3RAIV/NG AND DESIGNING.

thickr hus the virtual diameter of the pulley would be the nor I diameter plus one thickness of the belt. For other calciiiations the thickness of the belt is so small it may be nei ected without much error. Exan i. — In the draughting- room at Sibley College i there is a alve-molion model driven by an electric motor. I The shaft A of the motor carries a pulley ij" diameter from | which passes a belt to a 15" pulley on a counter-shaft B. I This shaft car 5" in diameter connected by a belt to the ey of 30' diameter on the valve-motion n: The speed ot o R. P. M. Find the speed of the valve-motifi *. M., Fig. 171. From formu

N,

Substituting we get

50 A',

50

39 R. P.M.

Some Practknl Rules. — The width of belts should be about 25 per cent less than the face of the pulky. It has been demonstrated by experience that large pulleys and fast running belts are much more economical than small pulleys and slow-speed belts. All pulleys should be carefully centred and balanced on the shaft. Driving-pulleys carrying shifting-belts should have a perfectly flat surface. All other pulleys should have a convexity of \" to I2" of width; when curved the chord of the arc should be the same. For

BELT GEARING. 2^1 pulleys smaller than 12" wide, from f" to \" per foot of width should be used. Pulley diameters should be as large as can be used provided the belt speed is kept within 5000 feet per minute, ^hich is held to be the limit of speed for belt economy. With regard to the position of idle pulleys in relation to the driving-pulley Taylor says, "Idle pulleys work most satisfactorily when located on the slack side of the belt about one quarter away from the driving-pulley." Transmission of Power by Belts. — Let two pulleys A and B be connected by a belt with a tension equal to 7*,. Until force is applied at A tending to produce rotation of the pulleys, the tension 7", and T^ will be equal ; but as the force at A increases the tension in T^ will increase, and that in T^

will decrease until 7", — 7", = Z' = resistance to rotation at the rim of the pulley; i.e., when the belt is at the point of slipping, the ratio of 7", to T^ will be a maximum and = efa^ or 7", H- 7^, = efa. Where e is the base of the Naperian system of logarithms, /is the coefficient of friction = .3, /i is in n measure and = a in degrees X 0.0174. By logarithms we find that 7", -r- 7", = efa = log. T.-i-T^^ fa log. e = AlAlfci^ Example 2, — A six H.P. dynamo is to have a speed of 1450 R. P. M and has a 6" pulley on its shaft. Power is obtained from an engine fly-wheel running at 58 revolutions per minute. To obtain the required velocity ratio between the engine and dynamo, the diameter of the fly-wheel will have to be 25 times that of the dynamo pulley with direct connection ; but such a diameter would be practically impossible, so it will be necessary to install a counter-shaft. Let 18'' be the

ai* i^^-* WING AND DESIGNING. mosl Ic diameter for the largest pulley on the countershaft, the necessary speed of the counter-shaft will be = M *« ~ ^^^ ^' ^* ^- Between the engine and the diameter of the fly-wheel be 50" then its connectingpulley on the counter-shaft will be ~^ = 6" neaiiy.

To determir. dynamo with tl of 2; = to the ,

t necessary to connect the : wilt have to find the value the lower side of the belt.

First find the work done by the dynamo =6x 33,000 =

198,000 foot-lbs. per minute; the rim of the dynamo pulley 67c runs at — X MSo = 2277 feet per minute; therefore

= 87 lbs. Let the centres of the dynamo shaft and counter-shaft be ig feet apart, then (see Fig. 172)

2277

''dvv.^

BELT GEARING.

243

R "^ T o" — x" = — ; — = - — ^ = .04, and from a table of natural / 180 trig, functions we find that tan. .04 = 2.25^. a = 180** — 2* = 175.75, a xn n measure = 175.75 X 0.0174 = 3.05. Then log. T, -r- T, = .4343 X .3 X 3-05 = .3974; from a table of logarithms we find that .3974 is the log. of the number 2.50, therefore 7; -7- 7; = 2.50. Combining these equations thus : 2.50 7; - 2.50 7; = 87 X 2.5", 7; - 2.50 r, = o, 1.50 7; = 217.5, we find 217.5 "^ i-SO = MS* and allowing 70 lbs. per inch width of belt, then 145 -^ 70 = 2.06, say 2 J". Some Practical Rules for the Transmission of Power^ —

Richards gives the following rule for the size of driving-belts, which he says is near enough for all cases that arise in ordinary practice. rx W

H.P. =

(4)

Where V = the velocity of the belt in feet per minute. W = the width of the belt in feet. A = the area given to suit different conditions in the following table :

TABLE 30.

LBATHBR BELTS SINGLE THICKNESS. I H. P. On smooth iron pulleys 80 ft. On wooden pulleys 65 ft. On covered puUeys 50 ft.

GUM BELTS AVERAGE THICKNESS. I H.P. On smooth iron pulleys 60 ft. On wooden pulleys 50 ft. On covered pulleys 35 ft.

1

tliickt on pi high s[ through thi cushion. The folio responding worn of 320 lbs. per sq

DRAWING AND DESIG.V/NG. uld be made as wide as possible; they are often but never too wide. ss of Belts. — As belts increase in width their 3uld also increase. Double belts should be used iver 12" diameter. Large belts running at very as in electrical work, should have slots punched m in such manner and position as to prevent air

thickness of belt and cor1 on a safe working stress , ts, are given by Unwta:

Thickness ot belt..

iSo

For other rules and formulfe see Kent's Engineers' Pocket Book, page 876. For a safe working tension under ordinary conditions, many authorities allow only 45 lbs. per inch of width; but according to Mr. A. W. Smith, experiments have shown that a safe tension of 70 lbs. may be had per inch of width of belt.

Proportions of Pulleys (Figs. 173 and 174). — a = centre of set-screw from end of hub = ii, = 10" and /J, and df, = 6", and

BELT GEARING.

255

find the corresponding diameters of the opposite steps according to Smith's graphical method just explained in connection with Fig. 179. Second, make complete working drawings of one of the cone-pulleys, showing half longitudinal cross-section and half side elevation combined, and also a half end eleyation like Fig. 180. Scale &' = i foot.

PROPORTIONS OF CONE PULLEY.

Let / = thickness of edge of rim = a ;

h H R

thickness of hub = . 14 ^BD^ -[- J" from eq. (lO); length of hub = 1.43^; ^^ce radius = 5-fi.

The remaining dimensions may be taken from the follow-^ ing table.

TABLE 82. (Dimensions in inches.)

h

2

2*

— r3

4

5

6

8

10

12

16

a e

i

A

ji

1

A

A I

1

f

\

f

I

li

II

Ik

;i

»»

»}

i

k

k

*

I >

li

li

ij

If

18 1 A

2]

Rope Pulleys. — Rope pulleys are made of cast iron with grooved rims, as shown in Figs. 181 and 182. The angle of the groove is usually 45°. The grooves for guide pulleys are semicircular at the bottom, the radius of the curve being a little greater than the radius of the rope. The diameter of a.

HtJmxc AND DESKltllra.

BELT GEARING.

FOLLOWER

as" DKAWISG AiVD DESICXJXG. rope pulley measured to the centre of the rope should not be less than that given by the following rule: D, = {\oD -\- \(>)D. where ZJ, = the smallt;st diameter o{ the puUey: D = the diameter of the rope. As in the case of belt gearing, the slack side of the rope should be on top wherever possible, so as to increase the arc of contact between the rope and the pulley. Fig. iSi. This is the form of groove long used in GreM Britain. It has flat sides inclined to each other at from 45" to 60°.

The general practice in America is to use the form of groove shown in Fig. 182. where the sides are cur\'cd. This form allows the rope to rotate in the groove, distributing the wear over the entire surface of the rope, making it last longer than it docs in the Hat-^dcd groove. Exercise 88. — Make a drawing of the section of the rim of I a rope [till Icy with five grooves, as shown in Fig. 181. Diam. of rope to be if. Sail.- full sh€. Take the other dimensions from the following tabl^. TABLE 33.

1

"3/ 16 15/16

2ay

BELT GEARING.

m

!

â– A

mi,

u.

.-y — y J Ni "' 'he centre of the wheel. * T, 12" on each side toward = the number of arms; R = the wheel; b = the width , feathers, which may be = > of the teeth as shown at i in Fig. 193, or f the breadth of the teeth ured at the centre of the shaft and from I to \l at the rim. s or feathers B do not add '■much to the resistance of the arms to bending in the direction of the driving force, but they arc necessary to give lateral stiffness to the anus. Unwin gives B^ .3^. The feathers should be tapered to faciiit.ite the removal of the pattern from the Mnd. To determine the number of arms in a wheel. Low & Bevis t;ive , + 4. The nearest number divisible by 2 sliould be

J, I tnc _J of

TOO THE £> GEARING.

275

Unwin gives four arms for wheels not over 4 ft. in diameter* six arms for wheels of from 4 to 8 ft. in diameter, and eight arms for wheels from 8 to 16 ft. in diameter. Rims of Gear Wheels. — The usual rim sections are shown in Figs. 193 to 204. The section shown in Fig. 193 is commonly used in light wheels. The following proportions agree closely with most authorities on the subject: d = the thickness of the rim at the edge = .48/. The other proportions are shown in the figures. In the rims for bevel gears shown in Figs. 198 to 200 the thickest part of the rim should be ^d. Figs. 201 and 202 show examples of mortise gears for

Fig. 193.

Fig. 194. U b —A

Fig. 195. ' — b -- .1

Fig. 197.

Fig. 198.

Fig. 196.

Fig. 199.

spur and bevel wheels respectively; the mortise teeth are fixed either by wood keys as shown in Fig. 201, or by round iron pins as shown in Fig. 202. The proportions given in the figures agree closely with good practice.

176 JJXA»-/.\'G AXJ> DESJGNIXG. Shrt tgr- — When the rim of a wheel is wider than the teeth and extends towards the point so as to form an annular ring uniting the ends of the teeth, the teeth are said to be shrouded. Figs. 303 and 204 give two examples of shrouded teeth. By shrouding out to the pitch circle as shown in Fig. 203. teeth which arc no thicker at the root tlian at tht pitch circle can be strengtheacd about 100 per cent. In the pinion of a pair of gear wheels the shrouding may extend to the points of the teeth in Fig. 2041 this compensates for the weak form h in very small wheels, and prevents their failarc from re wear.

no.

Hubs of Gear Wheels. — Figs. 205, 306. and 207 give ex.imples of hub? to correspond to the examples of arms

shown ill Figs. iSo. 191. ami 19;. respectively. The thickness of metal surrounding the bore of a gear

TOOTHED CEARJNC.

277

wheel is given by Reuleaux =, w = ,4^ -{- .4" (when h = the width o( the arm measured at the centre of the wheel). The keyway should be cut the full length of the hub, and the metal reinforced over the keyway if the wheel is intended for heavy duty. In large wheels the hubs are sometimes strengthened by wrought-iron rings shrunk on both ends; the thickness is made = — , and the thickness of 2 the metal under the rings is |w. b = width of teeth.

In heavy wheels with a large an:iount of metal surrounding the bore, the hub is sometimes slotted across between the arms to give relief from initial. strains due to unequal contraction in cooling; these slots are then filled with metal strips, and the divided hub is held firmly together by the iron or iteel -Ang referred to above.

V^lt^'^^-

CHAPTER IX. VALVES. COCKS. AND OIUCUPS.

i

for regulating the flow of a

ito three classes: — (i) FlapI a hinge; (2) lift-valves, or to the seat ; (3) slide-valves. «at. The valve-face is that its seat when closed, 'oot-valves are used to hold

ValTes.— .A fluid through an o^ Prof. Cnwio di valves or those whk those which rise pe or those which tnor* part of the >-aU-e in Foot valve and Stn» the water in long suction-pipes; otherwise the pump would liavo to bo chart^eil evsn.- time before starting. Yhc >;r,ii;ier prorcc:? the valve from being choked with st.MK--; iT ,>t!;cr ?>'"ia*. The most common foot-valves arc lu.i.ic .'f two cist-iroTi bo\eMAWZSC AA'D DESICA'IA'C.

talvc oo top of B. This st}-Ie of clack is called a relief vt break r^*"^ Hr. Henry- Teague, of Lincoln, Englandt n •paper read before the last, of M. E. of England, in ll reported having used a 15" main clack «-ith a 5" sapple* mentaiy clack (or the purpose of reducing the very great concussion which was had by using the 15' dack aJonc, w-ith tbc result ttut even when the hand or the ear was placed oa the dack'box hardly a tremor or a sound was perceptible, /^b*^ the entrance to the This doublc-va[ve s almost complete freedom 1 from shocks even in 1, and therefore works vet}' quietly. | The main valve, nu i leather, forms the joint between the valve-box ai ler. E is the top and F is tbe bottom valve-ptatc, i... >gether with f-inch rivetS) and an opening in the centre . al to an area of about one half or one third that of the main opening. This auxiliary opening is fitted with the clack-valve C referred to above. It has an upper and a lower valve-plate, held together with the bolt H and fastened to the main valve with two screws at X. in plan and sectional elevation. The laps L should be made one tenth of the diameter of the respective valve-opc-nings. Exercise 96. — Make drawings of foot-valve and strainer shown in Fig. 207, and also an outside elevation of the valvebox and strainer. Scale j" = i foot. India-rubber Valve. — This valve (Fig, 208) consists of an india-rubber disk D, a brass grating or seat s, and a perforated brass guard. The rubber guard and valve are attached to the grating by a stud-bolt B. The purpose of the guard

VALUES, COCKS, ANU OIL-CUPS. 38l

VALVES, COCA'S, AND OIL-CUPS. 285 is to prevent the valve from rising too high. The perforations in the grating should not be large enough to cause much flexure of the rubber disk. The area of the grating should be

such that when the valve is closed the pressure does not exceed 40 lbs. per square inch. The thickness of the india-rubber disk for large valves — i.e., valves over 6" in diameter — in condensers and pumps should be f " to J". India-rubber valves are not good for pressures over 100 lbs. per square inch. Exercise 97, — Make a complete drawing of the india-rubber valve as shown in Fig. 208. Scale full size. The projection of the perforations in the conical guard is shown in Fig. 209. The following proportions represent good practice. Use the nearest ^V''* Unit = . 19 4/^ a = diameter of india-rubber disk = i5-5 of unit. b = thickness of the india-rubber disk = 1.6 r = thickness of the grating-lip = 1.75 d = diameter of the valve. e = depth of seat-body = 2.75 /■= diameter of stud-body = 2.75 ^= diameter of stud = 1.75 h = diameter of holding-down bolt = 1.25 k = depth of grating = 2.50 / = thickness of grating-rib = .65 iw= width of seat-lip = .75 n = diameter of guard = 12.00 Bzordse 98. — Make a complete drawing of an india-rubber disk-valve similar to Fig. 208. d = 10". Scale p" = i foot.

VALVES. COCKS, AND OIL-CUPS. 28$ Lift- or Wing-valves (Fig. 210). — These valves are usually made of brass. The essential features are a circular disk and seat. The edges between the disk and seat are bevelled to the angle of 45**, and are easily fitted and ground together. Springs or rods are used to close these valves when it is necessary to place them in a horizontal position. To give the valve a partial rotation and provide a new seating at each stroke the

wings are curved slightly, as shown at Fig. 211. The curving f is arbitrary, and may be projected as shown in the figure. The outside of the seat has usually a taper of \'* in \2'\ but is sometimes driven straight. The amount of the lift of the valve may be determined as follows :

Let

a = area of opening in seat ; d = diameter of opening in seat; L = lift of valve.

Then

a = .7854^' and L = .35^, (i) Taking a unit of proportion = .2 Vrf^then r = thickness of disk = 1.3 ; / = length of wings = 8 ; t = thickness of seat = i at small end. Exercise 99. — Draw the valve as shown in Fig. 210 to the dimenaions given. Scale full size . £l3cerd8e xoo. — Make drawing of the curved wing-valve as shown in Fig. 211. Scale full size. SfliniUe-vaives (Fig. 212). — These valves are guided centnllf by means of a spindle and bridge ; otherwise they are

DRAWING A,\D DESICNINO,

yAi.y£s, COCKS, and o/l-cups.

287

*»» DKAUrtyC ASD DBStGNIffG. simUar to the iring-valve. but used for light work in pumps. The wing-valTC aitd the ^ndle-valve are sometimes made with a flat seat and a leather face and also used for light duty in pumps, but have ao advantage over the bevelled metal edges. Let JI'(FigJ io)=the width of the bearing-edgcs measured perpendiculariy to the axis o( the valve, / = the maximum dif/_ vdX the crushb^ pressure per square inch on the narrow bevelled edges of the valve and seat. The greatest safe pressure per square inch for phosphorbronze is 3000 lbs.; for gun-metal, 2000 lbs.; cast iron, 1000 lbs. : and leather and india-rubber. 700 lbs. Kzerctse 101. — Make drawings of the spindle and valve as shown in Fig. 313. Scale fuU sise. Ball-valTes (Fig. :;i3'i. — These valves are much used in deep well-pumps and small fast-running pumps. To guide the lift of the ball it is surrounded by a cage with three or The Txhi should be as narrow as safety will pernot to interfere with the free flow of the fluid above . se.it. Gun-metal is the best material for the balls, ti them they should be made hollow. u^u.il proportions for the ball-valves are given Unit = .2 t'rf. . - di.uiietiT of ball = 1. 34//. .z. in-ii.If lii.imeicr of seat-casing = \.\2d. - tliKkTicss of b.ill-guide = ,g times unit. ilist.mce between guides =■a-\- ■^' .

Urn

r ribs

mit

. so .1

the

v.dvc

1\>

h-lit.

U-\

Vhc

290

DKAWING AND DESIGNING.

f g h k I t

length of seat-shank thickness of seat-flange

lift of valve thickness of ball-shell

= 3 times unit. = I •' = 1.2 " = 1.8 " = .\6d " = 1.2 "

These valves work best with a small lift. William M. Barr says that the lift of ball-valves should not exceed J". Exercise 102. — Make drawings similar. to those shown in Fig. 213. rf^= li". Scale i\ full size. Flat India-rubber Disk-valves. — Fig. 2 14 shows an ordinary example of this style of valve for cold water. The valve-seat and spindle are cast in one piece. The spindle is turned and polished, and the hole in the india-rubber disk is t*« larger than the diameter of the spindle. This allows free action of the valve. The valvc-seat is screwed into place with a pitch of eight threads to the inch, which may be maintained for ;ill sizes up t(^ 4.\'' diameter. Mr. \V. M. Barr gives the followinii dimension^ for india-rubber valves:

TAHI.K 3")

—

Diaineier.

ThickncM. 3"

Hole.

0"

4"

H

2\"

7"

V

3"

\"

A"

-. 1"

.'."

J"

-li

A

4"

4

T*

4l'

\"

»

5"

X'

h"

Springs give good results if made with No. 12 brass wire for 2" and 2^" valves; No. 10 wire for 3" and 3^" valves*

( DtA WIX6 AMD I K«. S £er 4 ' aad 4^ valves. Hic outsde dfameter of tlic m^ ■■T te = -S ^t^ of tbc valvenltsk. Five to sol coSs e eUstictty. -Main dnwings for tbc tndta-twliiier ftas-afelv 8. which gives 2500 for the former ATbJ aSK-ut :--00 for the latter; then

4/'

(^)

k

.-S^

VALVES, COCKS, AND OIL-CUPS. 295 The lift of the valve may be determined by formula (i)

3r winged lift-valves. The valve and its seat must pass hrough the valve-chest, so the opening should be made about :" larger than the outside diameter of the valve-seat. The length of the thread on the valve-stem is equal to :hc length of the nut -|- lift of valve -|- i" for clearance. * Exercise 105. — Make drawings of the stop-valve as shown n Fig. 2i6. . Scale 4!' = i foot. Make the diameter of the inlet 6f to the root of the Iiread, instead o^6" as shown in the figure. Boiler Check-valve. — Fig. 2 1 7 shows working drawings of le Foster Safety Boiler-check. Exercise 106. — Make drawing of the Foster Boiler-check & shown in Fig. 217. Scale, full size. Cocks. — Cocks are valves which operate with a rotary kotix>n. The most common style of cock is that which con^sts of a plug made in the form of a truncated cone rotating I a seat of the same shape cast on a pipe. In Fig. 218 /* is the plug, and C the casing or conical seat. > is the opening through the plug. By rotating the plug in nc direction the openings are brought in line with the inlet ! and outlet B of the pipe or casing. In this position the >ck is open. Further rotation through 90° in either direction ill bring the openings in the plug opposite the solid parts of le casing and close the valve. Exercise 107. — Make drawings of the blow-off zoo^ shown I Fig. 218, and in addition to the views given make a half actional plan and half sectional end view. Scale, full size. In Fig. 219 is shown a blow-off cock which 13 really a nng'Valvey opened and closed by a piston which in turn is op-

VALVES, COCKS, AND OIL-CUPS. 29?

DRA WING AND DESIGNING.

M

VALVES, COCKS, AND OIL-CUPS.

29^

;rated by means of compressed air. The wing-valve V\& held >n its seat by the steam- pressure in the boiler. When com>ressed air is introduced into the cylinder C through the pipe ° the piston is pushed against the valve, opening it and allow*

ig the contents of the boiler to blow through the cock into he discharge-pipe D. Exercise 108. — Make complete drawings as shown in Fig. 19. Scale, full size. Oil-cups. — There are many forms of oil-cups. Figs. 220

300

DRAWIXG AND DESIGNING.

to 225 inclusive show the construction of some of the oil-cupi used in the locomotives of the Lehigh .Valley Railway. Fig. 220 is one of the simplest forms of oil-cups. The material is brass, cast in one piece. When charged, the reser-

voir is filled with waste and oil. This cup is used on the link-hanger. Fi side edge of the valve and the bridge. Inside clearance hastens exhaust, delays compression, but has no effect on tfae cut-off or admission. Ovtrtravel is the distance the steam edge of the vah« travels after fully opening the port, as shown in Fig. JJJ, Plate I. It increases the sharpness of the cut-off, retards compression, and gives a later release. Cylinder Clearance is all that space between the faces of the piston and the valve when the piston is at the beginning of the stroke. Piston CUarance is the distance between the piston and the cylinder-head. This clearance is to prevent the piston from striking either cylinder-head when the brasses on the connecting-rod wear and cause lost motion. Point of Cut-off is the point on the crank-circle which the centre of the crank reaches when the valve cuts off the live steam from the cylinder, and for the remainder of the stroke utilizes the expansive power of the steam. (See Fig. 233, Plate I.) Compression of the steam follows the closing of the exhaust before the piston has completed its stroke. This is

done to obtain a yielding cushion for the reciprocating parts to come to a full stop without shock before beginning the return stroke. Expansion begins at the point of cut-off and continues to the point of exhaust. (See Figs. 233 to 235 in Plate

ENGINE DETAILS. 309 During this period the valve travels a distance equal to the outside lap plus the inside lap. The Allen-Richardson Balance-valve. — This is one of the most popular combination slide-valves and is used on locomotives, stationary and large marine engines. Fig, 227 \ clearly shows the different parts used in the construction of this valve. The balance is effected by means of four rect-

1

"T

— ii(—

n

9^

m^

â– t

il™™ — ^

-i— j™Mil

W " wm^

1 1*

W-- — -"' M

kJ II.: A\

JLl^i — ^

angular packing-strips 6' fitted into grooves on the top of the valve. Semi-elltptic springs ^are used to hold the packingstrips against the pressure>plate P when there is no steam in the chest, but when steam is admitted to the chest it forces the strips against the pressure- plate and sides of the grooves, foiming a steam-tight joint and preventing the steam from acting on that part of the top of the valve enclosed by the four packing-strips.

3IO

DRAWING AND DESIGNING.

Exercise no. — Make drawings as shown in Fig. 227, and also a half plan of the top. Scale 8" =^ i foot, The Allen feature of this valve is the supplementary port shown at A just above the exhaust-arch. By means of this additional port steam is admitted to the same steam-port in tile cylinder from both sides of the valve at the same tJnii;, thereby increasiiijj the steam-supply with short cut-offs. The advantages of this valve over the plain slide-valve and the

objections to it arc lowing societies: A, Western Railway Clul Association, 1S96; and Chas. McShane, • The American Balance is applied to any a steam-tight joint being I01 under side of the steam-chest cove.

the proceedings of the (olvol. 20, May 1899: The S97; Am. Railway M. M. .ocomotive up to Date" by de-valve. — The American slide-valve. It consists of between the valve and the excluding live-steam pressure from a given area. {Sec Fig. 228.) This joint is formed by a bevelled snap-ring which, when in place, is slightly expanded over a cone. The cone or cones are either cast with the valves or bolted to it, as circumstances require. The mechanical construction of the balance is: First, the cone or two cones, where necessity requires, are either bolted to or cast with the valve. The snap-rings, which are bevelled on their inner side to a corresponding degree with that of the cone, arc bored smaller in diameter than their required working diameter so that, by their being forced down on the cone by the placing of the steam-chest cover in position, the rings

Manager of Tlic

t Slide-

by Mr, J. T. Wil!

E.VUI.VE DETAILS. \ themselves are under tension and are thus supported by 'heir own elasticity when not under steam. The steam when

^tliTiittcd to the steam-chest exerts a pressure on the entire C'rcumferencc of the ring, which has a tendency to close it or ; its diameter, and owing to its bevelled face and the per of the cone the steam also acts to lift it. Hy careful

lonsideration of the operation of this ring, no\v being held by "the steam-pressure tightly against the face of the cone, it will at once be seen that all lateral wear is avoided, and the ring moves as a part of the cone or valve itself. It will also be noted that the ring is absolutely compelled to assume its working position by the pressure on its circumference. When is shut off from the engine and the engine allowed to IS in locomotives, the valve is free to leave its seat until

312

DRAWING AND DESIGNING,

the cone comes in contact with the cover. This affords pCT» feet and ample relief of the air which the piston is forcing from one end of the cylinder, and also a direct communication with the other end of the cylinder, in which a vacuum is being formed. The cylinders are therefore perfectly relieved! by allowing the valve to lift y off its seat. The bevelled feature in the ring renders the ring setf-sid

Fic. 329. porting when not under steam, and supported by the sted pressure when under steam, automatic adjustment for I wear, positive action under all conditions, and sclf-maintainq the steam-joint. It renders it possible also to duplicate t rings of respective sizes in repairs. Owing to the absence of lateral wear on the cones 1 rings can be duplicated at any future time. The greatest a of balance can be secured by this design, because it is lei affected by back or upward pressure. The valve in c

ENGINE DETAILS.

315

leave its seat must first expand the taper ring against the chest-pressure acting on its circumference. ' The features enumerated all depend upon the taper. Fig. 228 is a double-cone balance-valve used on locomo^ tives. The improved T ring, the invention of Mr. J. T. Wilson^ is clearly shown in the figure. » Fig. 229 is a single-cone balance-valve for use on com* pound stationary engines. A double-cone valve of this kind is in use on the Japanese cruiser '' Chtose/' the rings of which

Fig. 230. are three feet ten inches in diameter, while that in Fig. 229 is only twenty inches diameter. Exercise Xll. — Make drawings of Fig. 230 as shown. Scale 6'' = i foot. The Bilgram Diagram. — Among the many diagrams devised to determine quickly and accurately the position of the valve for any position of the crank, that due to Mr. Hugo Bilgram is one of the simplest and best.

^iwe-M-c Ma

^'S/CWA'd.

ENGINE DETAILS, 3' 5

In Plate I let AB represent the valve circle, equal in di^tixieter to the travel of the valve, and LI the centre-line of ^he crank rotating in the direction of the arrow. From B J^y off the angle EOB, equal to the angle of advance. At E describe the arc bgk with a radius equal to the inside lap, ^nd also the arc afd with a radius equal to the outside lap. Crank positions drawn tangent to these arcs at a^ by kj and d >vill give the points of cut-off, compression, release, and adniission respectively, as indicated in the figure. Let us follow the crank through one revolution, beginning mrith the dead-point A, In this position de is equal to the outside lead, and the valve has moved from its central position a distance Ee equal to the lap plus the lead. These relations are clearly shown in Fig. 231. ^ gives the distance which the valve has travelled from its central position, and at X the left-hand steam-port is shown open to steam an amount equal to the lead when the piston is at the beginning of its forward stroke, and the eccentric is connected directly to the valve, i.e., without a rocker. When the crank reaches the position V perpendicular to OE the valve will have travelled from its central position a distance equal to EO, This is the extreme position of its •'crward travel, as shown in Fig. 232. The maximum opening of t ' oort X to steam is equal to Of, and the overtravel to ifii the actual width of the steam-port being = Om, As the crank leaves L* the valve begins to return, and when the crank is at L* the distance of the valve from its central position is equal to the lap ab. Port X is now closed to steam, and cut-off is accomplished as shown in Fig. 233. When the crank is at V the right-hand steam-port is

3l6 DRAWIXG AND DESIGNING. closed to exhaust, and compression begins as shown at T, Fig. 234. When the crank reaches L' the valve is on the point of opening port X, Fig. 235, to release the steam which was under compression during the time the crank moved from V to Z.'. At crank position L we find, as shown in Fig. 236, that the valve is on the point of admitting steam to port Y, and at B the backward stroke of the piston begins, the valve having opened the port an amount equal to the lead de, equal

to the opening shown at ^in Fig. 231. At crank position /' and valve position Fig. 237 the valve has attained its maximum travel in the opposite direction to that shown in Fig. 232. At /', Fig. 238, the valve cuts off steam from port K, and at A the new forward stroke begins.

~90%Sln>fic-Eiercise II2 — (Fig. 239.) Given. Required Travel = 5''- Outside lap. Angle of advance- . ■= 30°, Inside lap. Cut-off = 80* of stroke. Outside lead. Compression = go!f of stroke. Inside lead. Width of steam-port = \\' . Maximum port opening. Overt ravel.

ENGINE DETAILS. 31/ Draw AB and CO at right angles to one another. Describe the valve-circle arc ACB with a radius equal to half the travel or eccentricity of the eccentric = 2\'' to the scale ^i twice full size. From B lay off the angle EOB equal to the angle of advance = 30^. Let AB represent the stroke^ ^d from A lay off Al = 80^ of a stroke of 24^^ and erect a perpendicular to cut the valve circle in /'. Draw OD through ^'; this is the crank position at the point of cut-off. Through ^ perpendicular to OU draw Ea. With centre E and radius Em, describe the lap circle afd. From A lay off A2 = goj^ of th^ stroke, and erect a perpendicular to cut the valve circle ^t 6. Through b draw OD^ which is the crank position at the point of compression. With E as centre and Eb as radius describe the inside lap circle. Draw OD tangent to bgk at point k. At O with a radius = the port opening describe the arc h. Then Ea is the required lap, Eb the inside lap, de the lead, ke the inside lead. Of the maximum port-opening, and 4/ the overtravel.

Exercise 1x3. — (Fig. 240.) Given. Required. Cut-off = 80^ of stroke. Travel of the valve. Lap = \" . Angle of advance. Lead = ^'. Draw to a scale equal to twice full size AB and CO at right angles. Draw OU^ the position of crank at cut-off. Draw line I 2 parallel to AB at a distance above it equal to the lead id. Draw line 3 4 parallel to ^^ at a distance equal to the lap plus the lead above it. With a radius equal to the

I

3l8 DRAWING AND DESIGNING. 1

given lap find by trial a centre on the line 3 4, and drawthe 1

lap circle afd tangent to OU. and line I 2 at the points « 1

1 .,i

L^

'--—-■^J,—.

\/

y\. \^

1/

A^^-j. \

1/

/ -V"''^ \ /

1 ^'

/-^ e ft

â–

^P Fic.

Then through E with centre describe the valve circle

ACB.

AB is the travel of the valve, and BOB the angle c/ad-

Vance.

Fic. 241. Exercise 114 — (Fig. 241.) Given, RL'»u.retS. Cut-off = So;* of the stroke- Iravel of the ualve Admission = 90^ of the stroke. Lead. Maximum port-opening = t?/ (Fig. 240). Angle oJ Aijvsncft Lap

i^„

^

ENGINE DETAILS.

319'

Draw AB and CO at right angles. Draw OL^ the position of the crank at the point of admission. Draw OD^ the crank position at cut-off, and arc / with a radius equal to the given maximum port-opening. Bisect the angle LOD with the line OE, The centre, of the lap-circle will be on this^ line. Draw fm perpendicular to OV, and make fn = fm. Through / draw/ii parallel to nm, and aE parallel to mf. £ is the centre of lap circle. Through E describe the valve circle ACB, and draw the line Ee at right angles to AB, Then AB is the travel of the valve, Ea the lap, BOE the angle of advance^ and de the lead.

Fig. 24a. Exercise lis* — (Fig. 242.) Given. Required. Cut-ofi = 8oj< of the stroke. Angle of advance. Lead = i". Lap. Maximum port-opening = 0/(Fig. 240). Travel of valve. Draw AB and CO at right angles. Locate the crank position OV. Draw the lead-line i 2 at a distance de from AB and parallel to it. With centre O describe arc 3 4 with a radius equal to the maximum port-opening. Find by trial the centre £ of a circle that can be Jrawn tangent to (?Z*, arc 3 4, and line i 2. Through this centre draw OE.

3K> DRAWING AND DESIGNING.

1

Then BOE is the angle of advance, Ea the lap, and twice OE is equal to the travel of the valve. The Zeuner Valve Diagram — In Plate II let AB represent the stroke of the piston, the circle ACBD the path o( the crank-pin, and L the centre-line of the crank. From C lay off OE equal to the angle of advance, and on OE as a diameter describe the valve circle equal to half the travel of the valve or eccentricity of the eccentric when no rocker is used. From centre draw the arcs abc and gfk equal to the outside and inside laps respectively. At the beginning of liie forward stroke the true position of the crank would coincide with AO, and the centre-line ol the eccentric with OE. Now since the position of the point E is fixed for a given eccentricity and angle of advance, the point E will always be found on the circumference of the circle having OE as a diameter; and if the valve circle together with the crank be rotated around the centre (? in a direction opposite to the arrow, its intersection with the line OB from will be the distance which the valve has travelled from its central position after the crank has moved through any given angle. But instead of rotating the crank and valve circle let them remain fixed and rotate the line OB as an imaginary crank in the direction of the arrow, and the same results will be obtained in a much simpler way. Draw OL, the imaginary crank, through the point where the lap arc abc intersects the valve circle at the point c. The position of the valve will then be at the point of admission, because the valve will have travelled from its central position a distance equal to Oc, equal to the lap.

M

EUGiNE DETAILS.

322 DRAWING AND DESIGNING.

This is clearly shown in Fig. 343. The valve is travelling in a direction opposite to the imaginary crank, and the steam edge / of the valve is on the point of admitting steam to the port X just before the beginning of the forward stroke. When the imaginary crank reaches the position OB the valve will have travelled a distance equal to Oc from its central position and, OB being a dead-centre, the valve will havs opened the port A' to steam an amount equal to the lead, and the port Kto exhaust an amount equal to pq, Fig. 244. When the crank has reached the position OE the valve will then have attained the extreme position of its travel. The shaded part bi shows the full opening of the steam-port, and ke the amount of ovcrtravel, and at the same time the port Y is fully open to exhaust, as shown by the shaded portion//, andyi^is the exhaust ovcrtravel (Fig. 245). The valve now returns and at R begins to close port X, until when the crank arrives at /.' tiie port is fully closed and cut-ofT takes place, as shown in Fig, 246, When the crank is in the position V at right angles to OE the valve is in its middle position, as shown in Fig. 247. At the crank position V the valve has travelled a distance Og from its central position, and the port A" is about to open to exhaust, as shown in Fig. 248. The port continues to open, until at the position /,' the port is fully open and continues so until the crank reaches the position L', when it begins to close, and is fully closed when the crank reaches V. Now compre^nion begins and continues through the angle L'OL. At L the valve has returned to the point of admission a little before the beginning of the new forward stroke. At crank position L' it will be seen from Fig. 250 that the

iHfc.

ENGINE DETAILS.

323

port Fis fully open to steam, the port X fully open to exhaust, and that the valve has reached the extreme position of its travel for the backward stroke — ^just the opposite of the posi-

tion shown in Fig. 245.

-90%Sirohe-

Fig. 252. Exercise 116. — (Fig. 252). Assume the same conditions as in Ex. 112 for the Bilgram diagram. Draw AB and CO at right angles. Make AB to any convenient scale equal to the stroke of the piston, and let ACB represent the path of the crank-pin. From C lay off angle OE equal to the angle of advance = 30®, with a scale equal to twice full size. On Ok as a diameter, equal to half the travel of the valve, or 2\", describe the valve circle Oakc, From B lay off Bl equal to 8oj^ of the stroke, and erect a perpendicular to cut the crank-pin arc in Z*. Draw (?Z', the position of the crank at cut-off. Through the point a^ where OV cuts the valve circle, with O as centre describe the arc abc. From B lay off B2 equal to yoi> of the stroke, and erect a perpendicular to Z*. Draw OU, and through the point gy where OL* intersects the valve circle, with O as centre describe the arc gfh. From b lay off bk equal to the width of the steam-port, and with centre O and radius Ok describe the arc '^k^.

324

DRAWING A/fD DESIGNING,

Then Oa is the required lap, Og the inside lap, dt the lead. Sf the inside or exhaust lead, OE the maximum portopening, and KE the overtravel.

Exercise 117. — (Fig. 253.) Assunie the same conditions as given in Ex. 113. Draw AB and CO at right angles. Draw OL'. the crank position at cut-off. From O describe arc abc with a radiui equal to the lap, scale as before. Lay off de equal to the lead. Bisect Oa and Oc, and the point /where the bisectors

intersect will be the centre of the valve circle which may now be drawn through the points aOe. Then OE is equal to half the travel of the valve, and COR is the angle of advance. Exercise 118.— (Fig. 254.)

Point of cut-off. . . :^ 80* of stroke. Point of admission = 90^ of stroke. Lead = |". Draw AB and CO at right angles, tions OL and 0L\ Bisect the angle LOD with the line OE. On OE assume any point as g, and draw gf perpendicular to OB, and gh perpendicular to OL. With center O and radius Ok describe the arc he.

Required. Travel of valve. Lap. Angle of advance. Draw the crank posi-

ENGINE DETAILS.

325

Now the angles gOB and gOL are constant for a given admission and cut-oS ; therefore the lead will vary directly as the eccentricity.

Fio. 354. Let Og\>^ an assumed eccentricity, then ,',

n>

II

2j

A

'!

,;

IH

iS",

"i

n

â– 'i

af

fcj

:i

'f

It)

iq

14

1^

=i

7i

a

â– m

u

32

"A

aij

41

17

3(

3

I

Bt

a

ai

«i 3

.1

1

BNCtNE DETAILS.

^

ENGIN'E DETAILS. 337 held together by rivets. This piston is made by the Baldwin Locomotive Works for the '' Vauclain" compound locomotive. Bzerdae X28* — Make drawings as shown in Fig. 269. {Scale 4," = / foot.) Fig. 270 shows the cast-iron pistons used in tandem stationary engines built by Mcintosh & Seymour. The packing is composed of cast-iron spring-rings cut and kept in place by the method shown in detail in the figure. The arrangement for securing the rod is shown in detail in Fig, 68, page 103. Bxercise 129* — Make drawings as shown in Fig. 270. iScaU 3" =: I foot.) Fig. 271 is a built-up piston for the Tangye stationary

engines made by the Buckeye Engine Co. It consists of a spider, follower, and adjusting-screws. There are no springs ; the screws act on an uncut junk-ring, so can only be used for •centring, not for packing. The packing-rings are turned larger than the bore of the cylinder so as to pack by their own elasticity. They may or may not be turned eccentric, that is, thin where cut, and full thickness opposite the cut. If made eccentric, it is for the reason that they will be more nearly round when sprung into the cylinder. Exercise 130. — Make drawings as shown in Fig. 271. {Scale 6" = / foot.) Fig. 272 shows a water-piston suitable for cylinders under 9" diameter. The piston-rod is fitted to the head with a shoulder to drive the piston, and the rod is secured in place by a nut. The follower is also held by a nut and lock-nut. By this

1538 VAAIV/.VG AND DESIGNING.

UNCOMPflESSEOj

ENGINE DETAILS. 339 ans the follower and packing may be adjusted or renewed will. The packing is made of layers of cotton cloth and Jet rubber. Exercise 131. — Make drawings of water-piston as shown Fig. 272. {Scale full size,) Connecting-rods. — In steam and other engines the con* ting-rod connects the rotating cranlcwith the reciprocatcross-head. There are many styles of connecting-rods, and various Lhods are employed for taking up the wear of the brasses. ;s. 273 to 276 show good examples of rods used in station, locomotive, and marine engines of the most modern les.

Fig- 273 is the rod used by the Buckeye Engine Co. for ir ** Tangye " type of engine. The crank end is solidy the sses are lined with babbitt, and adjustment for wear is had means of a tapered steel block and screws. The crossd end is called a strap end. The strap is firmly bound to end of the rod with a cotter-key and gib, which also cons the adjustment for wear. Fig. 274 has strap ends front and back. Keys are ined between the straps and the rod to prevent the shear of strap-bolts. The construction of this rod and the method cloyed to take up the wear are plainly shown in the figure. i Erie City Iron Works use this rod on their stationary ines. Exercise 132. — Make the drawings as shown in Fig. 273. xle &' = / foot,) Exercise 133 — Make the drawings as shown in Fig. 274,

J4P

• A.W DESIGNING,

ENGINE DETAILS,

"!£*■-«^',

342 DRAWmc AND DESIGNING. except that half of the plan shall be a section through XX. {Scale &' = I fool.) Fig. 275 is the connecting-rod used by the Pennsylvanii Railroad Company on their fast passenger-locomotives. Tht crank end of this rod is an improved design invented by Mr. A. S. Vogt, mechanical engineer of the company. He explains the improvements as follows: As before, the back end of the rod is forked, but ihe

method of closing the open end of the fork is entirely different, and the key for closing the main brasses has been moved from the forward side of the brass to the rear, which has another good cHect, viz., as the brasses in both front end and back end of the rod wear and are closed up to meet thd wear, the actual length of the rod changes but very little, tor the reason that the keying of both ends is in the same direction, whereas in the old form of the rod the keying w opposite directions, and as a matter of course the distance from centre of crank-pin to centre of crosshead pin increased gradually. Tlie open end of the fork in this rod is closed, first, by a U-shaped block, the detail of which is marked A on Fig. 275 ; next, by the key which is marked ^ : and last ( of all by a combined key and bolt marked C; this bolt clamping the two members of the fork against the block A and forming an enclosed surface for the key to drive against. To ^ircvent the slacking up of the nut C, a keeper-block is provided at the bottom of the lower member of the fork. This ii , made with a recess into which the nut fits and a set-screw for locking the nut. The same keeper-block extends forward to the key B. which is also blocked by a set-screw in the block. It is quite evident that there is much less chance of sheariiig

SNCJ/fE DETAILS.

L^

344 DRAWING AND DESIGNING. or offsetting of the bolt and the key in this than there was of the bolt in the former design ; but even if it should take place, which is not very likely, the whole thing can readily be disconnected by, first, driving the key B out, unscrewing the nut on the bolt and moving the whole bolt slightly forward, when it can be lifted out at the top. Exercise 134. — Make drawings as shown in Fig, 11%, {Scale 6" = i foot.) This form of rod is called a marine connecting-rod because it is often used on marine engines, but it is also largely used on stationary engines and is occasionally seen on loco> motives. The crank-pin end or stub is usually forged solidly on the rod, and all but the sides is finished by turning in the lathe.

The sides are then planed and the bolt-holes drilled. The ' hole to receive the brasses may now be bored unless the top and bottom of the brasses are to be thicker than the sides, in which event the hole will not be completed until after the cap or top end of the stub has been slotted off and bolted on again. It will be seen that the bolts are turned down to a diameter equal to the diameter at the bottom of the threads. This does not weaken the bolt, but makes it more elastic. The cross-head end of this rod is made forked to suit the cross-head, but it will hi seen that each half of the forked end is constructed the same as in the large end. A detail dra-.ving of the bolt and its locking arrangement is given in Fig. 65, page 96, Exercise 135. — Make drawings as shown in Fig, 276. {Scale 2" — t foot.)

Jill

ENGINE DETAILS, 345 Thrust of Connecting-rod. — Assuming that a connect^'^g-rod is equal to a pillar rounded or jointed at both ends, ^^t ZP = diameter of piston in inches ; JL = length of stroke in inches ; / = length of connecting-rod in inches ; P =• maximum steam-pressure per square inch; T = thrust of connecting-rod. When the crank-pin is on a dead-centre and the connect^'^g-rod is in line with the piston-rod, then 4 ^He total load on the piston. But as the crank rotates the "Connecting rod becomes inclined to the centre line of motion, ^nd 7" increases as the angle of the connecting-rod increases Until a maximum is reached at half-stroke, provided the steam is not cut off before. The value of T may be found for any position of the

crank as lollows: Let AB, Fig. 277, be the connecting-rod, and BC the crank. * The forces acting at A are Wy the maximum pressure on the piston, and /?, the reaction of the guide on the crosshead, and y, the thrust along the connecting-rod. From the triangle of forces T _AB W^ AC and

AC VAB'-AC i/,'_£ ^4/*'-/' 4

346

DRAWING AND DESIGNING.

Diameter of Connecting-rodi Circular Section. — ^Thunton gives d = a^ Dl, i^P+C=: diameter at middle,

where a

_ (o.i (o.o

5 for fast engines, 08 for moderate speed ; for fast engines, J" for moderate speed ; /, = length of connecting-rod in feet. Seatons, Marks, and Whitham give rf= o. 02758 -/z?/VS

Fig. 277. For the diameter at the crank-pin end Whitham gives i.oS times the diameter at the cross head end. The rod is larger at the middle and tapers about i" to the foot. Sennett gives diameter at middle = — VP\

( lenglli of connecting-rod to throw of crank. Tiic U:iL;tli M connecting-rod is generally made equal to times tile iliiow of craiik. The cap is in the condition of a ■.mi on wliich the load is distributed over its entire surface. /■/ Tiled the bending moment is -7, and the moment of re•laiicc to bending is ^^/~. Therefore

ENGINE DETAILS. 355 from which

=V1

X /X6 ,. • • • • U)

X 8 X/' where L is: length of cap ;

T = thickness of cap ; P' = total load on cap ; / = distance between cap-studs ; /= strength of the material, which may be taken at 5CXX) lbs. Diameter of Studs. — The maximum pressure (/') on the under side of the cap is resisted by the studs CB. Therefore their effective area will be found by the formula Area at bottom of thread =

where n = number of studs ; yj = strength of material = 5000 lbs. per square inch of area at bottom of threads. Having found the area at the bottom of the threads, turn to Table No. 8, page 66, from which take the nearest diameter of screw having the required area. The diameter of the adjusting-studs {A) and the set-screws {s) may be made f" in diameter when the journal is 6" or less, and increased \" for every inch the journal is increased above 6" in j^iameter. The Gibs. — The height of the gibs {G) should be f, and their thickness at / should be equal to |, of the shaft diameter. Adjusting-wedges.-^Instead of using three adjusting wedges and screws, as in Fig. 280, another arrangement is to

35* DSAWIXG ASD Df-JIGXIKQ. use one wedge and one adjusting- screw with two guide pios, as in Fig. 282, In the latter airangcmcnt the wedge sapports the gib and is in contact with the frame its entire leoglk ILe thickness of the wedges at the top should be 1} times tlic Hisjnctcr of the screw {A^ â– \- \', and their width a/ whea

n^cd â–

,il (At.

Til,

.Ilk] not be lcs5 tlian \ the letigth of the taper of llic wedges may be made from i

ill 6 to I in 8. Tlic screw A should be sufficiently long to enter the wedge Jl'a distance equal to its diameter when the wodge is full down. Top and Bottom Blocks.— The thickness / at the thinII. -.t p.irt of the bottom block should be equal to .23, and tli.it of the top block .15, of the journal diameter.

ENGINE DETAILS, 357 Exercise 137. — Design a crank-shaft bearing of the form shown in Fig. 279, proportioned for a horizontal steamengine, having a cylinder 9" in diameter, stroke 10", initial steam-pressure 200 lbs. per square inch, and the diameter of the journal {D) 4". The bearing to have a vertical and horizontal adjustment of f". Show a HALF ELEVATION, A HALF SECTIONAL ELEVATION, a HALF END VIEW, a HALF SECTIONAL END VIEW, a HALF PLAN, and a HALF SECTIONAL PLAN of the right-hand side. Scale S" to the foot. Exercise 138. — Design a crank-shaft bearing of the form shown in Fig. 280, proportioned for a horizontal steamengine having a cylinder 18" in diameter, stroke 30" long, and an initial steam-pressure 'of 220 lbs. per square inch. The bearing to have a horizontal adjustment of J" in either direction and a vertical adjustment of |^". Make D the diameter of the journal 9". Show an ELEVATION, PART PLAN, and PART SECTIONAL PLAN, the plane of section passing through the centre of journal. Scale 4!' to the foot. Show also a detail drawin^i^ of the adjusting screws and wedges, as in Fig. 281. Scale